Finite Reductive Groups

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Representation Theory Of Finite Reductive Groups

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Author : Marc Cabanes
language : en
Publisher: Cambridge University Press
Release Date : 2004-01-29

Representation Theory Of Finite Reductive Groups written by Marc Cabanes 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 2004-01-29 with Mathematics categories.

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Representations Of Reductive Groups

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Author : Roger W. Carter
language : en
Publisher: Cambridge University Press
Release Date : 1998-09-03

Representations Of Reductive Groups written by Roger W. Carter 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 1998-09-03 with Mathematics categories.

This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.

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.

Representations Of Finite Groups Of Lie Type

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Author : François Digne
language : en
Publisher: Cambridge University Press
Release Date : 1991-04-26

Representations Of Finite Groups Of Lie Type written by François Digne 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 1991-04-26 with Mathematics categories.

The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne-Lusztig induction. This will be the first elementary treatment of this material in book form and will be welcomed by beginning graduate students in algebra.

Fourier Transforms Of Invariant Functions On Finite Reductive Lie Algebras

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Author : Emmanuel Letellier
language : en
Publisher: Springer
Release Date : 2004-11-15

Fourier Transforms Of Invariant Functions On Finite Reductive Lie Algebras written by Emmanuel Letellier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-15 with Mathematics categories.

The Fourier transforms of invariant functions on finite reductive Lie algebras are due to T.A. Springer (1976) in connection with the geometry of nilpotent orbits. In this book the author studies Fourier transforms using Deligne-Lusztig induction and the Lie algebra version of Lusztig’s character sheaves theory. He conjectures a commutation formula between Deligne-Lusztig induction and Fourier transforms that he proves in many cases. As an application the computation of the values of the trigonometric sums (on reductive Lie algebras) is shown to reduce to the computation of the generalized Green functions and to the computation of some fourth roots of unity.

Representations Of Sl2 Fq

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Author : Cédric Bonnafé
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-08

Representations Of Sl2 Fq written by Cédric Bonnafé and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-08 with Mathematics categories.

Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provides the simplicity required for a complete description of the theory, but also the richness needed for illustrating the most delicate aspects. The development of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representation theory. To this end, the author makes use of fundamental results of l-adic cohomology. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, with particular attention to the construction of quotients by various finite groups. At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. With the provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well as researchers and lecturers with an interest in Deligne-Lusztig theory.

Finite Reductive Groups Related Structures And Representations

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Author : Marc Cabanes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Finite Reductive Groups Related Structures And Representations written by Marc Cabanes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Finite reductive groups and their representations lie at the heart of group theory. This volume treats linear representations of finite reductive groups and their modular aspects together with Hecke algebras, complex reflection groups, quantum groups, arithmetic groups, Lie groups, symmetric groups and general finite groups.

Representations Of Algebraic Groups

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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Representations Of Algebraic Groups written by Jens Carsten Jantzen 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 2003 with Mathematics categories.

Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.

Pseudo Reductive Groups

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Author : Brian Conrad
language : en
Publisher: Cambridge University Press
Release Date : 2015-06-04

Pseudo Reductive Groups written by Brian Conrad 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 2015-06-04 with Mathematics categories.

This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. This second edition has been revised and updated, with Chapter 9 being completely rewritten via the useful new notion of 'minimal type' for pseudo-reductive groups.

The Character Theory Of Finite Groups Of Lie Type

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Author : Meinolf Geck
language : en
Publisher: Cambridge University Press
Release Date : 2020-02-27

The Character Theory Of Finite Groups Of Lie Type written by Meinolf Geck 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 2020-02-27 with Mathematics categories.

Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.