Counting Real Conjugacy Classes In Some Finite Classical Groups

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Counting Real Conjugacy Classes In Some Finite Classical Groups

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Author : Elena Amparo
language : en
Publisher:
Release Date : 2018

Counting Real Conjugacy Classes In Some Finite Classical Groups written by Elena Amparo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Conjugacy classes categories.

An element $g$ in a group $G$ is real if there exists $x\in G$ such that $xgx^{-1}=g^{-1}$. If $g$ is real then all elements in the conjugacy class of $g$ are real. In \cite{GS1} and \cite{GS2}, Gill and Singh showed that the number of real $\mathrm{GL}_n(q)$-conjugacy classes contained in $\mathrm{SL}_n(q)$ equals the number of real $\mathrm{PGL}_n(q)$-conjugacy classes when $q$ is even or $n$ is odd. In this paper, we use generating functions to show that the result is also true for odd $q$. We then follow the methods of \cite{GS1} and \cite{GS2} to count the number of real $\mathrm{U}_n(q)$ conjugacy classes contained in $\mathrm{SU}_n(q)$ and the number of real conjugacy classes in $\mathrm{PGU}_n(q)$, and we show that these are equal to the analogous quantities for $\mathrm{GL}_n(q)$ and $\mathrm{PGL}_n(q)$. Thus, we show that these four sets of conjugacy classes have equal size for all $n,q$.

A Course In Finite Group Representation Theory

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Author : Peter Webb
language : en
Publisher: Cambridge University Press
Release Date : 2016-08-19

A Course In Finite Group Representation Theory written by Peter Webb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-19 with Mathematics categories.

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Level One Algebraic Cusp Forms Of Classical Groups Of Small Rank

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Author : Gaëtan Chenevier
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-08-21

Level One Algebraic Cusp Forms Of Classical Groups Of Small Rank written by Gaëtan Chenevier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Mathematics categories.

The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of GLn over Q of any given infinitesimal character, for essentially all n≤8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain semisimple Z-forms of the compact groups SO7, SO8, SO9 (and G2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level one self-dual automorphic representations of GLn with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.

Conjugacy Classes In Semisimple Algebraic Groups

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Author : James E. Humphreys
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Conjugacy Classes In Semisimple Algebraic Groups written by James E. Humphreys and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Education categories.

Provides a useful exposition of results on the structure of semisimple algebraic groups over an arbitrary algebraically closed field. After the fundamental work of Borel and Chevalley in the 1950s and 1960s, further results were obtained over the next thirty years on conjugacy classes and centralizers of elements of such groups.

Classical Groups Derangements And Primes

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Author : Timothy C. Burness
language : en
Publisher: Cambridge University Press
Release Date : 2016-01-15

Classical Groups Derangements And Primes written by Timothy C. Burness and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-15 with Mathematics categories.

A graduate-level introduction to finite classical groups featuring a comprehensive account of the conjugacy and geometry of elements of prime order.

Asymptotic Counting In Conformal Dynamical Systems

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Author : Mark Pollicott
language : en
Publisher: American Mathematical Society
Release Date : 2021-09-24

Asymptotic Counting In Conformal Dynamical Systems written by Mark Pollicott and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-24 with Mathematics categories.

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Automorphism Orbits And Element Orders In Finite Groups Almost Solubility And The Monster

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Author : Alexander Bors
language : en
Publisher: American Mathematical Society
Release Date : 2023-07-31

Automorphism Orbits And Element Orders In Finite Groups Almost Solubility And The Monster written by Alexander Bors and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.

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Characters Of Reductive Groups Over A Finite Field Am 107 Volume 107

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Author : George Lusztig
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

Characters Of Reductive Groups Over A Finite Field Am 107 Volume 107 written by George Lusztig and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.

This book presents a classification of all (complex) irreducible representations of a reductive group with connected centre, over a finite field. To achieve this, the author uses etale intersection cohomology, and detailed information on representations of Weyl groups.

The Solution Of The K Gv Problem

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Author : Peter Schmid
language : en
Publisher: Imperial College Press
Release Date : 2007

The Solution Of The K Gv Problem written by Peter Schmid and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

The k(GV) conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product GV is bounded above by the order of V . Here V is a finite vector space and G a subgroup of GL(V) of order prime to that of V . It may be regarded as the special case of Brauer''s celebrated k(B) problem dealing with p -blocks B of p-solvable groups ( p a prime). Whereas Brauer''s problem is still open in its generality, the k(GV) problem has recently been solved, completing the work of a series of authors over a period of more than forty years. In this book the developments, ideas and methods, leading to this remarkable result, are described in detail. Sample Chapter(s). Chapter 1: Conjugacy Classes, Characters, and Clifford Theory (296 KB). Contents: Conjugacy Classes, Characters and Clifford Theory; Blocks of Characters and Brauer''s k(B) Problem; The k(GV) Problem; Symplectic and Orthogonal Modules; Real Vectors; Reduced Pairs of Extraspecial Type; Reduced Pairs of Quasisimple Type; Modules Without Real Vectors; Class Numbers of Permutation Groups; The Final Stages of the Proof; Possibilities for k(GV) = V Some Consequences for Block Theory; The Non-Coprime Situation. Readership: Postgraduate students and researchers with background and research interests in group and representation theory.

Groups And Computation Ii

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Author : Larry Finkelstein, William M. Kantor
language : en
Publisher: American Mathematical Soc.
Release Date :

Groups And Computation Ii written by Larry Finkelstein, William M. Kantor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Algebra categories.

Consists of papers presented at the workshop on Groups and Computation held at DIMACS.