Modular Representations of Finite Groups of Lie Type

James E. Humphreys - Collection London Mathematical Society Lecture Notes

240 pages, parution le 23/03/2006

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Résumé

Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne-Lusztig characters. One goal has been to make the subject more accessible to those working in neighbouring parts of group theory, number theory, and topology. Core material is treated in detail, but the later chapters emphasize informal exposition accompanied by examples and precise references.

This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic
Core material is covered in detail, while other topics and recent developments are surveyed
One goal has been to make the subject more accessible to those working in neighboring parts of group theory, number theory, and topology: chapters are accompanied by examples and carefully selected references

Sommaire

Finite groups of Lie type
Simple modules
Weyl modules and Lusztig's conjecture
Computation of weight multiplicities
Other aspects of simple modules
Tensor products
BN-pairs and induced modules
Blocks
Projective modules
Comparison with Frobenius kernels
Cartan invariants
Extensions of simple modules
Loewy series
Cohomology
Complexity and support varieties
Ordinary and modular representations
Deligne-Lusztig characters
The groups G2
General and special linear groups
Suzuki and Ree groups

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	James E. Humphreys
Collection	London Mathematical Society Lecture Notes
Parution	23/03/2006
Nb. de pages	240
Format	15,5 x 22,5
Couverture	Broché
Poids	360g
Intérieur	Noir et Blanc
EAN13	9780521674546
ISBN13	978-0-521-67454-6