Imprimitive Irreducible Modules For Finite Quasisimple Groups

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Imprimitive Irreducible Modules For Finite Quasisimple Groups

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Author : Gerhard Hiss
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-06

Imprimitive Irreducible Modules For Finite Quasisimple Groups written by Gerhard Hiss 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 2015-02-06 with Mathematics categories.

Motivated by the maximal subgroup problem of the finite classical groups the authors begin the classification of imprimitive irreducible modules of finite quasisimple groups over algebraically closed fields K. A module of a group G over K is imprimitive, if it is induced from a module of a proper subgroup of G. The authors obtain their strongest results when char(K)=0, although much of their analysis carries over into positive characteristic. If G is a finite quasisimple group of Lie type, they prove that an imprimitive irreducible KG-module is Harish-Chandra induced. This being true for \rm char(K) different from the defining characteristic of G, the authors specialize to the case char(K)=0 and apply Harish-Chandra philosophy to classify irreducible Harish-Chandra induced modules in terms of Harish-Chandra series, as well as in terms of Lusztig series. The authors determine the asymptotic proportion of the irreducible imprimitive KG-modules, when G runs through a series groups of fixed (twisted) Lie type. One of the surprising outcomes of their investigations is the fact that these proportions tend to 1, if the Lie rank of the groups tends to infinity. For exceptional groups G of Lie type of small rank, and for sporadic groups G, the authors determine all irreducible imprimitive KG-modules for arbitrary characteristic of K.

Imprimitive Irreducible Modules For Finite Quasisimple Groups

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Author : G. Hiss
language : en
Publisher:
Release Date : 2014

Imprimitive Irreducible Modules For Finite Quasisimple Groups written by G. Hiss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Algebraic fields categories.

Motivated by the maximal subgroup problem of the finite classical groups we begin the classification of imprimitive irreducible modules of finite quasisimple groups over algebraically closed fields K. A module of a group G over K is imprimitive, if it is induced from a module of a proper subgroup of G. We obtain our strongest results when char(K) = 0, although much of our analysis carries over into positive characteristic. If G is a finite quasisimple group of Lie type, we prove that an imprimitive irreducible KG-module is Harish-Chandra induced. This being true for char(K) different from the defining characteristic of G, we specialize to the case char(K) = 0 and apply Harish-Chandra philosophy to classify irreducible Harish-Chandra induced modules in terms of Harish-Chandra series, as well as in terms of Lusztig series. We determine the asymptotic proportion of the irreducible imprimitive KG-modules, when G runs through a series groups of fixed (twisted) Lie type. One of the surprising outcomes of our investigations is the fact that these proportions tend to 1, if the Lie rank of the groups tends to infinity. For exceptional groups G of Lie type of small rank, and for sporadic groups G, we determine all irreducible imprimitive KG-modules for arbitrary characteristic of K.

Finite Simple Groups Thirty Years Of The Atlas And Beyond

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Author : Manjul Bhargava
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-24

Finite Simple Groups Thirty Years Of The Atlas And Beyond written by Manjul Bhargava 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 2017-07-24 with Biography & Autobiography categories.

Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.

Surveys In Combinatorics 2021

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Author : Konrad K. Dabrowski
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-24

Surveys In Combinatorics 2021 written by Konrad K. Dabrowski 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 2021-06-24 with Mathematics categories.

These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.

The Maximal Subgroups Of The Low Dimensional Finite Classical Groups

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Author : John N. Bray
language : en
Publisher: Cambridge University Press
Release Date : 2013-07-25

The Maximal Subgroups Of The Low Dimensional Finite Classical Groups written by John N. Bray 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 2013-07-25 with Mathematics categories.

Classifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.

Irreducible Geometric Subgroups Of Classical Algebraic Groups

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Author : Timothy C. Burness,
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-25

Irreducible Geometric Subgroups Of Classical Algebraic Groups written by Timothy C. Burness, 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 2016-01-25 with Mathematics categories.

Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .

Irreducible Almost Simple Subgroups Of Classical Algebraic Groups

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Author : Timothy C. Burness
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-06-26

Irreducible Almost Simple Subgroups Of Classical Algebraic Groups written by Timothy C. Burness 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 2015-06-26 with Mathematics categories.

Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.

Symmetry Breaking For Representations Of Rank One Orthogonal Groups

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Author : Toshiyuki Kobayashi
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-27

Symmetry Breaking For Representations Of Rank One Orthogonal Groups written by Toshiyuki Kobayashi 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 2015-10-27 with Mathematics categories.

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.

Reduced Fusion Systems Over 2 Groups Of Sectional Rank At Most 4

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Author : Bob Oliver
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-01-25

Reduced Fusion Systems Over 2 Groups Of Sectional Rank At Most 4 written by Bob Oliver 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 2016-01-25 with Mathematics categories.

The author classifies all reduced, indecomposable fusion systems over finite -groups of sectional rank at most . The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional -rank at most . But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

Endoscopic Classification Of Representations Of Quasi Split Unitary Groups

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Author : Chung Pang Mok
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-04-09

Endoscopic Classification Of Representations Of Quasi Split Unitary Groups written by Chung Pang Mok 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 2015-04-09 with Mathematics categories.

In this paper the author establishes the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.