Representations of Finite Groups of Lie Type

François Digne; Jean Michel

doi:10.1017/9781108673655

Skip to main content Accessibility help

Home
Books
Representations of Finite Groups of Lie Type

Representations of Finite Groups of Lie Type

- Get access
  
  Buy a print copy
  
  Check if you have access via personal or institutional login
  
  Log in Register
Cited by 26
Cited by
- 26
Crossref Citations

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Geck, Meinolf and Malle, Gunter 2020. The Character Theory of Finite Groups of Lie Type.

CrossRef

Google Scholar

Lusztig, G. 2021. On induction of class functions. Representation Theory of the American Mathematical Society, Vol. 25, Issue. 13, p. 412.

CrossRef

Google Scholar

Lesesvre, Didier and Petrow, Ian 2022. The volumes of Miyauchi subgroups. Archiv der Mathematik, Vol. 119, Issue. 1, p. 37.

CrossRef

Google Scholar

Johansson, Birte 2022. On the inductive McKay–Navarro condition for finite groups of Lie type in their defining characteristic. Journal of Algebra, Vol. 610, Issue. , p. 223.

CrossRef

Google Scholar

Gurevich, Maxim 2023. A triangular system for local character expansions of Iwahori-spherical representations of general linear groups. Comptes Rendus. Mathématique, Vol. 361, Issue. G1, p. 21.

CrossRef

Google Scholar

Michel, Jean 2023. Tower equivalence and Lusztig’s truncated Fourier transform. Proceedings of the American Mathematical Society, Series B, Vol. 10, Issue. 23, p. 252.

CrossRef

Google Scholar

Liu, Zhengwei Palcoux, Sebastien and Ren, Yunxiang 2023. Interpolated family of non-group-like simple integral fusion rings of Lie type. International Journal of Mathematics, Vol. 34, Issue. 06,

CrossRef

Google Scholar

BRIDGER, NICK and KAMGARPOUR, MASOUD 2023. CHARACTER STACKS ARE PORC COUNT. Journal of the Australian Mathematical Society, Vol. 115, Issue. 3, p. 289.

CrossRef

Google Scholar

Hoyer, Linda and Nebe, Gabriele 2023. Orthogonal determinants of $${\textrm{SL}\,}_3(q)$$ and $${\textrm{SU}\,}_3(q)$$. Archiv der Mathematik, Vol. 121, Issue. 5-6, p. 681.

CrossRef

Google Scholar

Hetz, Jonas 2023. On the generalised Springer correspondence for groups of type 𝐸₈. Representation Theory of the American Mathematical Society, Vol. 27, Issue. 26, p. 973.

CrossRef

Google Scholar

Shu, Cheng 2023. E-Polynomials of Generic -Character Varieties: Branched Case. Forum of Mathematics, Sigma, Vol. 11, Issue. ,

CrossRef

Google Scholar

Malle, Gunter and Navarro, Gabriel 2023. Height zero conjecture with Galois automorphisms. Journal of the London Mathematical Society, Vol. 107, Issue. 2, p. 548.

CrossRef

Google Scholar

Geck, Meinolf 2023. The character table of the finite Chevalley group $$F_4(q)$$ for q a power of 2. Archiv der Mathematik, Vol. 121, Issue. 5-6, p. 669.

CrossRef

Google Scholar

Li, Tzu‐Jan and Shotton, Jack 2023. On endomorphism algebras of Gelfand–Graev representations II. Bulletin of the London Mathematical Society, Vol. 55, Issue. 6, p. 2876.

CrossRef

Google Scholar

SPÄTH, BRITTA 2023. EXTENSIONS OF CHARACTERS IN TYPE D AND THE INDUCTIVE MCKAY CONDITION, I. Nagoya Mathematical Journal, Vol. 252, Issue. , p. 906.

CrossRef

Google Scholar

Larsen, Michael Taylor, Jay and Tiep, Pham Huu 2023. Character bounds for regular semisimple elements and asymptotic results on Thompson’s conjecture. Mathematische Zeitschrift, Vol. 303, Issue. 2,

CrossRef

Google Scholar

Li, Conghui 2023. Restrictions of irreducible characters of finite groups of Lie type to derived subgroups and regular semisimple elements. Communications in Algebra, Vol. 51, Issue. 3, p. 983.

CrossRef

Google Scholar

Feng, Zhicheng and Späth, Britta 2023. Unitriangular basic sets, Brauer characters and coprime actions. Representation Theory of the American Mathematical Society, Vol. 27, Issue. 6, p. 115.

CrossRef

Google Scholar

MULLER, JOSEPH 2023. COHOMOLOGY OF THE BRUHAT–TITS STRATA IN THE UNRAMIFIED UNITARY RAPOPORT–ZINK SPACE OF SIGNATURE. Nagoya Mathematical Journal, Vol. 250, Issue. , p. 470.

CrossRef

Google Scholar

Arote, Prashant and Mishra, Manish 2023. Prasad’s Conjecture About Dualizing Involutions. International Mathematics Research Notices,

CrossRef

Google Scholar

Download full list

2nd edition
François Digne, Université de Picardie Jules Verne, Amiens, Jean Michel, Centre National de la Recherche Scientifique (CNRS), Paris

Publisher:: Cambridge University Press
Online publication date:: February 2020
Print publication year:: 2020
Online ISBN:: 9781108673655
DOI:: https://doi.org/10.1017/9781108673655

Subjects:: Mathematics (general), Mathematics, Algebra
Series:: London Mathematical Society Student Texts (95)

Information

Contents

Metrics

On its original publication, this book provided the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis–Alvis duality map and Mackey's theorem and the results that can be deduced from it, before moving on to a discussion of Deligne–Lusztig induction and Lusztig's Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.

References

Metrics

Altmetric attention score

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Representations of Finite Groups of Lie Type

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Book description

Refine List

Actions for selected content:

Contents

Frontmatter
pp i-vi

Contents
pp v-viii

Introduction to the Second Edition
pp 1-1

From the Introduction to the First Edition
pp 2-4

1 - Basic Results on Algebraic Groups
pp 5-18

2 - Structure Theorems for Reductive Groups
pp 19-38

3 - (B,N)-Pairs; Parabolic, Levi, and Reductive Subgroups; Centralisers of Semi-simple Elements
pp 39-58

4 - Rationality, the Frobenius Endomorphism, the Lang–Steinberg Theorem
pp 59-78

5 - Harish-Chandra Theory
pp 79-90

6 - Iwahori–Hecke Algebras
pp 91-112

7 - The Duality Functor and the Steinberg Character
pp 113-129

8 - ℓ-Adic Cohomology
pp 130-136

9 - Deligne–Lusztig Induction: The Mackey Formula
pp 137-147

10 - The Character Formula and Other Results on Deligne–Lusztig Induction
pp 148-160

11 - Geometric Conjugacy and the Lusztig Series
pp 161-195

12 - Regular Elements; Gelfand–Graev Representations; Regular and Semi-Simple Characters
pp 196-224

13 - Green Functions
pp 225-241

14 - The Decomposition of Deligne–Lusztig Characters
pp 242-248

References
pp 249-254

Index
pp 255-258

Metrics

Altmetric attention score

Full text views

Book summary page views

Representations of Finite Groups of Lie Type

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Altmetric attention score

Full text views

Book summary page views