The Finite Irreducible Linear 2 Groups Of Degree 4

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The Finite Irreducible Linear 2-Groups of Degree 4

Dane Laurence Flannery
The Finite Irreducible Linear 2 Groups of Degree 4 Book PDF

Author : Dane Laurence Flannery
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 51,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806258

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The Finite Irreducible Linear 2-Groups of Degree 4 by Dane Laurence Flannery Pdf

This memoir contains a complete classification of the finite irreducible 2-subgroups of $GL(4, {\mathbb C})$. Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by a generating set of monomial matrices. The problem is treated by a variety of techniques, including elementary character theory, a method for describing Hasse diagrams of submodule lattices, and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups, and Schur indices of their defining characters, are also considered.It's features include: a complete classification of a class of $p$-groups; a first step towards extending presently available databases for use in proposed 'soluble quotient algorithms'; and, groups presented explicitly; may be used to test conjectures or to serve generally as a resource in group-theoretic computations.

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl
Algebro Geometric Quasi Periodic Finite Gap Solutions of the Toda and Kac van Moerbeke Hierarchies Book PDF

Author : Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 41,9 Mb
Release : 1998
Category : Evolution equations, Nonlinear
ISBN : 9780821808085

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Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies by Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl Pdf

In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived. Features: Simple and unified treatment of the topic. Self-contained development. Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.

The Siegel Modular Variety of Degree Two and Level Four

Ronnie Lee,Steven H. Weintraub,Jerome William Hoffman
The Siegel Modular Variety of Degree Two and Level Four Book PDF

Author : Ronnie Lee,Steven H. Weintraub,Jerome William Hoffman
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 45,5 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821806203

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The Siegel Modular Variety of Degree Two and Level Four by Ronnie Lee,Steven H. Weintraub,Jerome William Hoffman Pdf

The Siegel Modular Variety of Degree Two and Level Four is by Ronnie Lee and Steven H. Weintraub: Let $\mathbf M_n$ denote the quotient of the degree two Siegel space by the principal congruence subgroup of level $n$ of $Sp_4(\mathbb Z)$. $\mathbfM_n$ is the moduli space of principally polarized abelian surfaces with a level $n$ structure and has a compactification $\mathbfM^*_n$ first constructed by Igusa. $\mathbfM^*_n$ is an almost non-singular (non-singular for $n> 1$) complex three-dimensional projective variety (of general type, for $n> 3$). The authors analyze the Hodge structure of $\mathbfM^*_4$, completely determining the Hodge numbers $h^{p,q} = \dim H^{p,q}(\mathbfM^*_4)$. Doing so relies on the understanding of $\mathbfM^*_2$ and exploitation of the regular branched covering $\mathbfM^*_4 \rightarrow \mathbfM^*_2$.""Cohomology of the Siegel Modular Group of Degree Two and Level Four"" is by J. William Hoffman and Steven H. Weintraub. The authors compute the cohomology of the principal congruence subgroup $\Gamma_2(4) \subset S{_p4} (\mathbb Z)$ consisting of matrices $\gamma \equiv \mathbf 1$ mod 4. This is done by computing the cohomology of the moduli space $\mathbfM_4$. The mixed Hodge structure on this cohomology is determined, as well as the intersection cohomology of the Satake compactification of $\mathbfM_4$.

Model Theory and Linear Extreme Points in the Numerical Radius Unit Ball

Michael A. Dritschel,Hugo Jan Woerdeman
Model Theory and Linear Extreme Points in the Numerical Radius Unit Ball Book PDF

Author : Michael A. Dritschel,Hugo Jan Woerdeman
Publisher : American Mathematical Soc.
Page : 62 pages
File Size : 44,5 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806517

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Model Theory and Linear Extreme Points in the Numerical Radius Unit Ball by Michael A. Dritschel,Hugo Jan Woerdeman Pdf

This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented: A complete description of the linear extreme points of the $n\times n$ matrix (numerical radius) unit ball Several equivalent characterizations of matricial extremals in the unit ball; that is, those members which do not allow a nontrivial extension remaining in the unit ball Applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks In addition, an explicit construction for unitary 2-dilations of unit ball members is given, Ando's characterization of the unit ball is further developed, and a study of operators satisfying $ A - \mathrm{Re} (e^{i\theta}A)\geq 0$ for all $\theta$ is initiated.

Finite and Locally Finite Groups

B. Hartley,G.M. Seitz,A.V. Borovik,R.M. Bryant
Finite and Locally Finite Groups Book PDF

Author : B. Hartley,G.M. Seitz,A.V. Borovik,R.M. Bryant
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401103299

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Finite and Locally Finite Groups by B. Hartley,G.M. Seitz,A.V. Borovik,R.M. Bryant Pdf

This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni

Matching of Orbital Integrals on GL(4) and GSp(2)

Yuval Zvi Flicker
Matching of Orbital Integrals on GL 4 and GSp 2 Book PDF

Author : Yuval Zvi Flicker
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 40,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809594

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Matching of Orbital Integrals on GL(4) and GSp(2) by Yuval Zvi Flicker Pdf

The trace formula is the most powerful tool currently available to establish liftings of automorphic forms, as predicted by Langlands principle of functionality. The geometric part of the trace formula consists of orbital integrals, and the lifting is based on the fundamental lemma. The latter is an identity of the relevant orbital integrals for the unit elements of the Hecke algebras. This volume concerns a proof of the fundamental lemma in the classically most interesting case of Siegel modular forms, namely the symplectic group $Sp(2)$. These orbital integrals are compared with those on $GL(4)$, twisted by the transpose inverse involution. The technique of proof is elementary. Compact elements are decomposed into their absolutely semi-simple and topologically unipotent parts also in the twisted case; a double coset decomposition of the form $H\backslash G/K$--where H is a subgroup containing the centralizer--plays a key role.

Diagram Groups

Victor Guba,Mark Sapir
Diagram Groups Book PDF

Author : Victor Guba,Mark Sapir
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 41,5 Mb
Release : 1997
Category : Geometric group theory
ISBN : 9780821806395

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Diagram Groups by Victor Guba,Mark Sapir Pdf

Diagram groups are groups consisting of spherical diagrams (pictures) over monoid presentations. They can be also defined as fundamental groups of the Squier complexes associated with monoid presentations. The authors show that the class of diagram groups contains some well-known groups, such as the R. Thompson group F. This class is closed under free products, finite direct products, and some other group-theoretical operations. The authors develop combinatorics on diagrams similar to the combinatorics on words. This helps in finding some structure and algorithmic properties of diagram groups. Some of these properties are new even for R. Thompson's group F. In particular, the authors describe the centralizers of elements in F, prove that it has solvable conjugacy problems, etc.

Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders

Lindsay Childs
Hopf Algebras Polynomial Formal Groups and Raynaud Orders Book PDF

Author : Lindsay Childs
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 50,5 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821810774

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Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders by Lindsay Childs Pdf

This book gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.

Lie Groups and Subsemigroups with Surjective Exponential Function

Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert
Lie Groups and Subsemigroups with Surjective Exponential Function Book PDF

Author : Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert
Publisher : American Mathematical Soc.
Page : 189 pages
File Size : 50,8 Mb
Release : 1997
Category : Exponential functions
ISBN : 9780821806418

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Lie Groups and Subsemigroups with Surjective Exponential Function by Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert Pdf

In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.

Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras

Michael David Weiner
Bosonic Construction of Vertex Operator Para Algebras from Symplectic Affine Kac Moody Algebras Book PDF

Author : Michael David Weiner
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 45,7 Mb
Release : 1998
Category : Kac-Moody algebras
ISBN : 9780821808665

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Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras by Michael David Weiner Pdf

Begins with the bosonic construction of four level -1/2 irreducible representations of the symplectic affine Kac-Moody Lie algebra Cl. The direct sum of two of these is given the structure of a vertex operator algebra (VOA), and the direct sum of the other two is given the structure of a twisted VOA-module. The dissertation includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type Dl. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Wandering Vectors for Unitary Systems and Orthogonal Wavelets

Xingde Dai,David R. Larson
Wandering Vectors for Unitary Systems and Orthogonal Wavelets Book PDF

Author : Xingde Dai,David R. Larson
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 53,7 Mb
Release : 1998
Category : Functional analysis
ISBN : 9780821808009

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Wandering Vectors for Unitary Systems and Orthogonal Wavelets by Xingde Dai,David R. Larson Pdf

Investigates topological and structural properties of the set W(U) of all complete wandering vectors for a system U of unitary operators acting on a Hilbert space. The authors parameterize W(U) in terms of a fixed vector y and the set of all unitary operators which locally commute with U at y. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities

Arne Meurman,Mirko Primc
Annihilating Fields of Standard Modules of mathfrak sl 2 mathbb C sim and Combinatorial Identities Book PDF

Author : Arne Meurman,Mirko Primc
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 51,6 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809235

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Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities by Arne Meurman,Mirko Primc Pdf

In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde{\mathfrak g}$, they construct the corresponding level $k$ vertex operator algebra and show that level $k$ highest weight $\tilde{\mathfrak g}$-modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level $k$ standard modules and study the corresponding loop $\tilde{\mathfrak g}$-module--the set of relations that defines standard modules. In the case when $\tilde{\mathfrak g}$ is of type $A^{(1)}_1$, they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of Rogers-Ramanujan type combinatorial identities.

Limit Theorems for Functionals of Ergodic Markov Chains with General State Space

Xia Chen
Limit Theorems for Functionals of Ergodic Markov Chains with General State Space Book PDF

Author : Xia Chen
Publisher : American Mathematical Soc.
Page : 225 pages
File Size : 44,8 Mb
Release : 1999
Category : Central limit theorem
ISBN : 9780821810606

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Limit Theorems for Functionals of Ergodic Markov Chains with General State Space by Xia Chen Pdf

This book is intended for graduate students and research mathematicians working probability theory and statistics.

Some Connections between Isoperimetric and Sobolev-type Inequalities

Serguei Germanovich Bobkov,Christian Houdré
Some Connections between Isoperimetric and Sobolev type Inequalities Book PDF

Author : Serguei Germanovich Bobkov,Christian Houdré
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 48,5 Mb
Release : 1997
Category : Gaussian processes
ISBN : 9780821806425

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Some Connections between Isoperimetric and Sobolev-type Inequalities by Serguei Germanovich Bobkov,Christian Houdré Pdf

For Borel probability measures on metric spaces, this text studies the interplay between isoperimetric and Sobolev-type inequalities. In particular the question of finding optimal constants via isoperimetric quantities is explored. Also given are necessary and sufficient conditions for the equivalence between the extremality of some sets in the isoperimetric problem and the validity of some analytic inequalities. The book devotes much attention to: the probability distributions on the real line; the normalized Lebesgue measure on the Euclidean sheres; and the canonical Gaussian measure on the Euclidean space.

The Geometric Vein

C. Davis,B. Grünbaum,F.A. Sherk
The Geometric Vein Book PDF

Author : C. Davis,B. Grünbaum,F.A. Sherk
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461256489

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The Geometric Vein by C. Davis,B. Grünbaum,F.A. Sherk Pdf

Geometry has been defined as that part of mathematics which makes appeal to the sense of sight; but this definition is thrown in doubt by the existence of great geometers who were blind or nearly so, such as Leonhard Euler. Sometimes it seems that geometric methods in analysis, so-called, consist in having recourse to notions outside those apparently relevant, so that geometry must be the joining of unlike strands; but then what shall we say of the importance of axiomatic programmes in geometry, where reference to notions outside a restricted reper tory is banned? Whatever its definition, geometry clearly has been more than the sum of its results, more than the consequences of some few axiom sets. It has been a major current in mathematics, with a distinctive approach and a distinc ti v e spirit. A current, furthermore, which has not been constant. In the 1930s, after a period of pervasive prominence, it appeared to be in decline, even passe. These same years were those in which H. S. M. Coxeter was beginning his scientific work. Undeterred by the unfashionability of geometry, Coxeter pursued it with devotion and inspiration. By the 1950s he appeared to the broader mathematical world as a consummate practitioner of a peculiar, out-of-the-way art. Today there is no longer anything that out-of-the-way about it. Coxeter has contributed to, exemplified, we could almost say presided over an unanticipated and dra matic revival of geometry.