Symmetry Breaking For Representations Of Rank One Orthogonal Groups

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Symmetry Breaking for Representations of Rank One Orthogonal Groups II

Toshiyuki Kobayashi,Birgit Speh
Symmetry Breaking for Representations of Rank One Orthogonal Groups II Book PDF

Author : Toshiyuki Kobayashi,Birgit Speh
Publisher : Springer
Page : 344 pages
File Size : 44,8 Mb
Release : 2018-12-27
Category : Science
ISBN : 9789811329012

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Symmetry Breaking for Representations of Rank One Orthogonal Groups II by Toshiyuki Kobayashi,Birgit Speh Pdf

This work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup.The study of symmetry breaking operators (intertwining operators for restriction) is an important and very active research area in modern representation theory, which also interacts with various fields in mathematics and theoretical physics ranging from number theory to differential geometry and quantum mechanics.The first author initiated a program of the general study of symmetry breaking operators. The present book pursues the program by introducing new ideas and techniques, giving a systematic and detailed treatment in the case of orthogonal groups of real rank one, which will serve as models for further research in other settings.In connection to automorphic forms, this work includes a proof for a multiplicity conjecture by Gross and Prasad for tempered principal series representations in the case (SO(n + 1, 1), SO(n, 1)). The authors propose a further multiplicity conjecture for nontempered representations.Viewed from differential geometry, this seminal work accomplishes the classification of all conformally covariant operators transforming differential forms on a Riemanniann manifold X to those on a submanifold in the model space (X, Y) = (Sn, Sn-1). Functional equations and explicit formulæ of these operators are also established.This book offers a self-contained and inspiring introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in representation theory, automorphic forms, differential geometry, and theoretical physics.

Symmetry Breaking for Representations of Rank One Orthogonal Groups

Toshiyuki Kobayashi,Birgit Speh
Symmetry Breaking for Representations of Rank One Orthogonal Groups Book PDF

Author : Toshiyuki Kobayashi,Birgit Speh
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 46,7 Mb
Release : 2015-10-27
Category : Banach spaces
ISBN : 9781470419226

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Symmetry Breaking for Representations of Rank One Orthogonal Groups by Toshiyuki Kobayashi,Birgit Speh Pdf

The authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of and . They construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explicitly. Symmetry breaking operators at exceptional discrete parameters are thoroughly studied. The authors obtain closed formulae for the functional equations which the composition of the symmetry breaking operators with the Knapp-Stein intertwining operators of and satisfy, and use them to determine the symmetry breaking operators between irreducible composition factors of the spherical principal series representations of and . Some applications are included.

Lie Theory and Its Applications in Physics

Vladimir Dobrev
Lie Theory and Its Applications in Physics Book PDF

Author : Vladimir Dobrev
Publisher : Springer Nature
Page : 526 pages
File Size : 52,7 Mb
Release : 2023-01-29
Category : Mathematics
ISBN : 9789811947513

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field. The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Representations of Reductive Groups

Monica Nevins,Peter E. Trapa
Representations of Reductive Groups Book PDF

Author : Monica Nevins,Peter E. Trapa
Publisher : Birkhäuser
Page : 532 pages
File Size : 47,7 Mb
Release : 2015-12-18
Category : Mathematics
ISBN : 9783319234434

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Representations of Reductive Groups by Monica Nevins,Peter E. Trapa Pdf

Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Song Huang, Toshiyuki Kobayashi, Bertram Kostant, Wenjing Li, George Lusztig, Eric Marberg, William M. McGovern, Wilfried Schmid, Kari Vilonen, Diana Shelstad, Peter E. Trapa, David A. Vogan, Jr., Nolan R. Wallach, Xiaoheng Wang, Geordie Williamson

Conformal Symmetry Breaking Operators for Differential Forms on Spheres

Toshiyuki Kobayashi,Toshihisa Kubo,Michael Pevzner
Conformal Symmetry Breaking Operators for Differential Forms on Spheres Book PDF

Author : Toshiyuki Kobayashi,Toshihisa Kubo,Michael Pevzner
Publisher : Springer
Page : 192 pages
File Size : 44,5 Mb
Release : 2016-10-11
Category : Mathematics
ISBN : 9789811026577

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Conformal Symmetry Breaking Operators for Differential Forms on Spheres by Toshiyuki Kobayashi,Toshihisa Kubo,Michael Pevzner Pdf

This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin–Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C∞-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in differential geometry, representation theory, and theoretical physics.

Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1

Vladimir Dobrev
Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 Book PDF

Author : Vladimir Dobrev
Publisher : Springer
Page : 427 pages
File Size : 43,5 Mb
Release : 2018-11-28
Category : Mathematics
ISBN : 9789811327155

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Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 by Vladimir Dobrev Pdf

This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19–25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and those focusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system.

Conformal Symmetry Breaking Differential Operators on Differential Forms

Matthias Fischmann,Andreas Juhl,Petr Somberg
Conformal Symmetry Breaking Differential Operators on Differential Forms Book PDF

Author : Matthias Fischmann,Andreas Juhl,Petr Somberg
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 41,9 Mb
Release : 2021-06-18
Category : Education
ISBN : 9781470443245

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Conformal Symmetry Breaking Differential Operators on Differential Forms by Matthias Fischmann,Andreas Juhl,Petr Somberg Pdf

We study conformal symmetry breaking differential operators which map dif-ferential forms on Rn to differential forms on a codimension one subspace Rn−1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn−1. They correspond to homomorphisms of generalized Verma mod-ules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F -method to derive explicit formulas for such homomorphisms. In particular, we find explicit formulas for the generators of the intertwining operators of the re-lated branching problems restricting generalized Verma modules for so(n +1, 1) to so(n, 1). As consequences, we derive closed formulas for all conformal symmetry breaking differential operators in terms of the first-order operators d, δ, d¯ and δ¯ and certain hypergeometric polynomials. A dominant role in these studies is played by two infinite sequences of symmetry breaking differential operators which depend on a complex parameter λ. Their values at special values of λ appear as factors in two systems of factorization identities which involve the Branson-Gover opera- tors of the Euclidean metrics on Rn and Rn−1 and the operators d, δ, d¯ and δ¯ as factors, respectively. Moreover, they naturally recover the gauge companion and Q-curvature operators of the Euclidean metric on the subspace Rn−1, respectively.

Overgroups of Root Groups in Classical Groups

Michael Aschbacher
Overgroups of Root Groups in Classical Groups Book PDF

Author : Michael Aschbacher
Publisher : American Mathematical Soc.
Page : 1840 pages
File Size : 42,7 Mb
Release : 2016-04-26
Category : Algebra
ISBN : 9781470418458

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Overgroups of Root Groups in Classical Groups by Michael Aschbacher Pdf

The author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of c-root subgroups.

Nil Bohr-Sets and Almost Automorphy of Higher Order

Wen Huang,Song Shao,Xiangdong Ye
Nil Bohr Sets and Almost Automorphy of Higher Order Book PDF

Author : Wen Huang,Song Shao,Xiangdong Ye
Publisher : American Mathematical Soc.
Page : 86 pages
File Size : 53,7 Mb
Release : 2016-04-26
Category : Automorphic functions
ISBN : 9781470418724

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Nil Bohr-Sets and Almost Automorphy of Higher Order by Wen Huang,Song Shao,Xiangdong Ye Pdf

Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d∈N does the collection of {n∈Z:S∩(S−n)∩…∩(S−dn)≠∅} with S syndetic coincide with that of Nild Bohr0 -sets? In the second part, the notion of d -step almost automorphic systems with d∈N∪{∞} is introduced and investigated, which is the generalization of the classical almost automorphic ones.

The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup

U. Meierfrankenfeld,Christian-Albrechts-University of Kiel, Kiel, Germany,,G. Stroth
The Local Structure Theorem for Finite Groups With a Large p Subgroup Book PDF

Author : U. Meierfrankenfeld,Christian-Albrechts-University of Kiel, Kiel, Germany,,G. Stroth
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 52,7 Mb
Release : 2016-06-21
Category : Finite groups
ISBN : 9781470418779

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The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup by U. Meierfrankenfeld,Christian-Albrechts-University of Kiel, Kiel, Germany,,G. Stroth Pdf

Let p be a prime, G a finite Kp-group S a Sylow p-subgroup of G and Q a large subgroup of G in S (i.e., CG(Q)≤Q and NG(U)≤NG(Q) for 1≠U≤CG(Q)). Let L be any subgroup of G with S≤L, Op(L)≠1 and Q⋬L. In this paper the authors determine the action of L on the largest elementary abelian normal p-reduced p-subgroup YL of L.

Geometric Methods in Physics XXXV

Piotr Kielanowski,Anatol Odzijewicz,Emma Previato
Geometric Methods in Physics XXXV Book PDF

Author : Piotr Kielanowski,Anatol Odzijewicz,Emma Previato
Publisher : Birkhäuser
Page : 282 pages
File Size : 42,5 Mb
Release : 2018-02-10
Category : Mathematics
ISBN : 9783319635941

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Geometric Methods in Physics XXXV by Piotr Kielanowski,Anatol Odzijewicz,Emma Previato Pdf

This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.

Moduli of Double EPW-Sextics

Kieran G. O'Grady
Moduli of Double EPW Sextics Book PDF

Author : Kieran G. O'Grady
Publisher : American Mathematical Soc.
Page : 172 pages
File Size : 43,9 Mb
Release : 2016-03-10
Category : Equations, Sextic
ISBN : 9781470416966

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Moduli of Double EPW-Sextics by Kieran G. O'Grady Pdf

The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of ⋀3C6 modulo the natural action of SL6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3[2] polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds.

Classification of $E_0$-Semigroups by Product Systems

Michael Skeide
Classification of E 0 Semigroups by Product Systems Book PDF

Author : Michael Skeide
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 47,5 Mb
Release : 2016-03-10
Category : Endomorphisms (Group theory)
ISBN : 9781470417383

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Classification of $E_0$-Semigroups by Product Systems by Michael Skeide Pdf

In these notes the author presents a complete theory of classification of E0-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.

Classes of Polish Spaces Under Effective Borel Isomorphism

Vassilios Gregoriades
Classes of Polish Spaces Under Effective Borel Isomorphism Book PDF

Author : Vassilios Gregoriades
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 46,8 Mb
Release : 2016-03-10
Category : Isomorphisms (Mathematics)
ISBN : 9781470415631

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Classes of Polish Spaces Under Effective Borel Isomorphism by Vassilios Gregoriades Pdf

The author studies the equivalence classes under Δ11 isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of Δ11-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.

The Fourier Transform for Certain HyperKahler Fourfolds

Mingmin Shen,Charles Vial
The Fourier Transform for Certain HyperKahler Fourfolds Book PDF

Author : Mingmin Shen,Charles Vial
Publisher : American Mathematical Soc.
Page : 161 pages
File Size : 48,6 Mb
Release : 2016-03-10
Category : Fourier transformations
ISBN : 9781470417406

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The Fourier Transform for Certain HyperKahler Fourfolds by Mingmin Shen,Charles Vial Pdf

Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH∗(A). By using a codimension-2 algebraic cycle representing the Beauville-Bogomolov class, the authors give evidence for the existence of a similar decomposition for the Chow ring of Hyperkähler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. They indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.