In this book Professor Lusztig solves an interesting problem by
entirely new methods: specifically, the use of cohomology of
buildings and related complexes. The book gives an explicit
construction of one distinguished member, D(V), of the discrete
series of GLn (Fq), where V is the n-dimensional F-vector space on
which GLn(Fq) acts. This is a p-adic representation; more precisely
D(V) is a free module of rank (q--1) (q2--1)...(qn-1--1) over the
ring of Witt vectors WF of F. In Chapter 1 the author studies the
homology of partially ordered sets, and proves some vanishing
theorems for the homology of some partially ordered sets associated
to geometric structures. Chapter 2 is a study of the representation
? of the affine group over a finite field. In Chapter 3 D(V) is
defined, and its restriction to parabolic subgroups is determined.
In Chapter 4 the author computes the character of D(V), and shows
how to obtain other members of the discrete series by applying
Galois automorphisms to D(V). Applications are in Chapter 5. As one
of the main applications of his study the author gives a precise
analysis of a Brauer lifting of the standard representation of
GLn(Fq).
General
Imprint: |
Princeton University Press
|
Country of origin: |
United States |
Series: |
Annals of Mathematics Studies |
Release date: |
October 1974 |
First published: |
October 1974 |
Authors: |
George Lusztig
|
Dimensions: |
229 x 152 x 6mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
104 |
ISBN-13: |
978-0-691-08154-0 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
Groups & group theory
|
LSN: |
0-691-08154-9 |
Barcode: |
9780691081540 |
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