Published January 30, 2006
by Cambridge University Press .
Written in English
London Mathematical Society Lecture Note Series
|The Physical Object|
|Number of Pages||250|
Modular Representations of Finite Groups of Lie Type by James E. Humphreys, , available at Book Depository with free delivery : James E. Humphreys. Modular representation theory is a branch of mathematics, and that part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory [citation. Representation stability also provides a framework in which to find and to predict patterns, from classical representation theory (Littlewood–Richardson and Murnaghan rules, stability of Schur functors), to cohomology of groups (pure braid, Torelli and congruence groups), to Lie algebras and their homology, to the (equivariant) cohomology of. This book is a unique survey of the whole field of modular representation theory of finite groups. The main topics are block theory and module theory of group representations, including blocks with cyclic defect groups, symmetric groups, groups of Lie type, local-global conjectures.
Cite this chapter as: Geck M., Hiss G. () Modular Representations of Finite Groups of Lie Type in Non-defining Characteristic. In: Cabanes M. (eds) Finite Reductive Groups: Related Structures and Representations. Books. Please feel free to use the PDF files below under the terms specified in the licenses. (Lectures on the representation theory of finite groups of Lie type, in Chinese) Planning. 代数学方法：卷二 (Methods of algebra: Volume 2, in Chinese) It will be published by the Higher Education Press (Beijing). 模形式初步. This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. 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 aim of the course was to introduce an audience consisting mainly of PhD students and postdoctoral researchers working in finite group theory and neighboring areas to results on the subgroup structure of linear algebraic groups and the related finite groups of Lie type. The final chapter is the representation theory of groups of Lie type, both in defining and non-defining characteristics. The first section deals with defining characteristic representations. 4 1. FINITE GROUPS OF LIE TYPE D (for ≥ 4), and 4 is unusual in having such automorphisms of both order 2 and order 3. The group of ﬁxed points is isomorphic to the group of rational points over Fq of a quasisplit but nonsplit group of the same type as G. Book Description: 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.