Descent Construction For Gspin Groups

Author : Joseph Hundley,Eitan Sayag
Publisher : American Mathematical Soc.
Page : 125 pages
File Size : 50,5 Mb
Release : 2016-09-06
Category : Descent
ISBN : 9781470416676

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Descent Construction for GSpin Groups by Joseph Hundley,Eitan Sayag Pdf

In this paper the authors provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of essentially self-dual representations, that is, representations which are isomorphic to the twist of their own contragredient by some Hecke character. The authors' theory supplements the recent work of Asgari-Shahidi on the functorial lift from (split and quasisplit forms of) GSpin2n to GL2n.

Author : David Ginzburg,Stephen Rallis,David Soudry
Publisher : World Scientific
Page : 350 pages
File Size : 47,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814304986

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The Descent Map from Automorphic Representations of GL(n) to Classical Groups by David Ginzburg,Stephen Rallis,David Soudry Pdf

This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of the Gelfand?Graev type, or of the Fourier?Jacobi type to certain residual Eisenstein series. An account of this automorphic descent, with complete, detailed proofs, leads to a thorough understanding of important ideas and techniques. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively self-contained, the content of some of the chapters can serve as topics for graduate students seminars.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,5 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9789814464949

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The Descent Map from Automorphic Representations of GL(n) to Classical Groups by Anonim Pdf

Author : Dihua Jiang,Freydoon Shahidi,David Soudry
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 45,8 Mb
Release : 2016-04-29
Category : Automorphic forms
ISBN : 9781470417093

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Advances in the Theory of Automorphic Forms and Their $L$-functions by Dihua Jiang,Freydoon Shahidi,David Soudry Pdf

This volume contains the proceedings of the workshop on “Advances in the Theory of Automorphic Forms and Their L-functions” held in honor of James Cogdell's 60th birthday, held from October 16–25, 2013, at the Erwin Schrödinger Institute (ESI) at the University of Vienna. The workshop and the papers contributed to this volume circle around such topics as the theory of automorphic forms and their L-functions, geometry and number theory, covering some of the recent approaches and advances to these subjects. Specifically, the papers cover aspects of representation theory of p-adic groups, classification of automorphic representations through their Fourier coefficients and their liftings, L-functions for classical groups, special values of L-functions, Howe duality, subconvexity for L-functions, Kloosterman integrals, arithmetic geometry and cohomology of arithmetic groups, and other important problems on L-functions, nodal sets and geometry.

Author : F. Dahmani,V. Guirardel,D. Osin
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 50,8 Mb
Release : 2017-01-18
Category : Hyperbolic groups
ISBN : 9781470421946

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Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces by F. Dahmani,V. Guirardel,D. Osin Pdf

he authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the latter one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, , and the Cremona group. Other examples can be found among groups acting geometrically on spaces, fundamental groups of graphs of groups, etc. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, the authors solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.

Author : Matthew J. Emerton
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 47,7 Mb
Release : 2017-07-13
Category : Geometry, Analytic
ISBN : 9780821875629

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Locally Analytic Vectors in Representations of Locally -adic Analytic Groups by Matthew J. Emerton Pdf

The goal of this memoir is to provide the foundations for the locally analytic representation theory that is required in three of the author's other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors (of various “radii of analyticity”). The author uses the analysis of these subspaces as one of the basic tools in his study of such representations. Thus in this memoir he presents a development of locally analytic representation theory built around this point of view. The author has made a deliberate effort to keep the exposition reasonably self-contained and hopes that this will be of some benefit to the reader.

Author : Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 52,8 Mb
Release : 2016-10-05
Category : 1-factorization
ISBN : 9781470420253

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Proof of the 1-Factorization and Hamilton Decomposition Conjectures by Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown Pdf

In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D≥2⌈n/4⌉−1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, χ′(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D≥⌊n/2⌋. Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree δ≥n/2. Then G contains at least regeven(n,δ)/2≥(n−2)/8 edge-disjoint Hamilton cycles. Here regeven(n,δ) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree δ. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case δ=⌈n/2⌉ of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.

Author : Xin-Rong Dai,Qiyu Sun
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 50,5 Mb
Release : 2016-10-05
Category : Gabor frames
ISBN : 9781470420154

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The $abc$-Problem for Gabor Systems by Xin-Rong Dai,Qiyu Sun Pdf

A longstanding problem in Gabor theory is to identify time-frequency shifting lattices aZ×bZ and ideal window functions χI on intervals I of length c such that {e−2πinbtχI(t−ma): (m,n)∈Z×Z} are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above abc-problem for Gabor systems.

Author : Toshihiko Masuda,Reiji Tomatsu
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 50,7 Mb
Release : 2016-10-05
Category : Conjugacy classes
ISBN : 9781470420161

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Rohlin Flows on von Neumann Algebras by Toshihiko Masuda,Reiji Tomatsu Pdf

The authors will classify Rohlin flows on von Neumann algebras up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II1 factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III0 factors. Several concrete examples are also studied.

Author : Hans Lundmark,Jacek Szmigielski
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 42,9 Mb
Release : 2016-10-05
Category : Discontinuous functions
ISBN : 9781470420260

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An Inverse Spectral Problem Related to the Geng-Xue Two-Component Peakon Equation by Hans Lundmark,Jacek Szmigielski Pdf

The authors solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperis-Procesi equations. Like the spectral problems for those equations, this one is of a ``discrete cubic string'' type-a nonselfadjoint generalization of a classical inhomogeneous string--but presents some interesting novel features: there are two Lax pairs, both of which contribute to the correct complete spectral data, and the solution to the inverse problem can be expressed using quantities related to Cauchy biorthogonal polynomials with two different spectral measures. The latter extends the range of previous applications of Cauchy biorthogonal polynomials to peakons, which featured either two identical, or two closely related, measures. The method used to solve the spectral problem hinges on the hidden presence of oscillatory kernels of Gantmacher-Krein type, implying that the spectrum of the boundary value problem is positive and simple. The inverse spectral problem is solved by a method which generalizes, to a nonselfadjoint case, M. G. Krein's solution of the inverse problem for the Stieltjes string.

Author : Brayton Gray
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 48,6 Mb
Release : 2017-02-20
Category : Abelian groups
ISBN : 9781470423087

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Abelian Properties of Anick Spaces by Brayton Gray Pdf

Anick spaces are closely connected with both EHP sequences and the study of torsion exponents. In addition they refine the secondary suspension and enter unstable periodicity. This work describes their -space properties as well as universal properties. Techniques include a new kind on Whitehead product defined for maps out of co-H spaces, calculations in an additive category that lies between the unstable category and the stable category, and a controlled version of the extension theorem of Gray and Theriault (Geom. Topol. 14 (2010), no. 1, 243–275).

Author : Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 51,8 Mb
Release : 2017-04-25
Category : Operator algebras
ISBN : 9781470423094

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Semicrossed Products of Operator Algebras by Semigroups by Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis Pdf

The authors examine the semicrossed products of a semigroup action by -endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

Author : Yves Le Jan,Michael B. Marcus,Jay Rosen
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 55,6 Mb
Release : 2017-04-25
Category : Gaussian processes
ISBN : 9781470436957

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Intersection Local Times, Loop Soups and Permanental Wick Powers by Yves Le Jan,Michael B. Marcus,Jay Rosen Pdf

Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of -th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.

Author : Steve Hofmann,Dorina Mitrea,Marius Mitrea
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 52,5 Mb
Release : 2017-01-18
Category : Function spaces
ISBN : 9781470422608

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$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets by Steve Hofmann,Dorina Mitrea,Marius Mitrea Pdf

The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.

Author : Isabel Averill,King-Yeung Lam,Yuan Lou
Publisher : American Mathematical Soc.
Page : 1060 pages
File Size : 46,7 Mb
Release : 2017-01-18
Category : Bifurcation theory
ISBN : 9781470422028

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The Role of Advection in a Two-Species Competition Model: A Bifurcation Approach by Isabel Averill,King-Yeung Lam,Yuan Lou Pdf

The effects of weak and strong advection on the dynamics of reaction-diffusion models have long been studied. In contrast, the role of intermediate advection remains poorly understood. For example, concentration phenomena can occur when advection is strong, providing a mechanism for the coexistence of multiple populations, in contrast with the situation of weak advection where coexistence may not be possible. The transition of the dynamics from weak to strong advection is generally difficult to determine. In this work the authors consider a mathematical model of two competing populations in a spatially varying but temporally constant environment, where both species have the same population dynamics but different dispersal strategies: one species adopts random dispersal, while the dispersal strategy for the other species is a combination of random dispersal and advection upward along the resource gradient. For any given diffusion rates the authors consider the bifurcation diagram of positive steady states by using the advection rate as the bifurcation parameter. This approach enables the authors to capture the change of dynamics from weak advection to strong advection. The authors determine three different types of bifurcation diagrams, depending on the difference of diffusion rates. Some exact multiplicity results about bifurcation points are also presented. The authors' results can unify some previous work and, as a case study about the role of advection, also contribute to the understanding of intermediate (relative to diffusion) advection in reaction-diffusion models.