Unitary representations of reductive Lie groups / David A. Vogan, Jr.

Format:

Book

Author/Creator:

Vogan, David A., 1954-

Series:

Annals of mathematics studies ; 118.

Annals of mathematics studies ; 118

Language:

English

Subjects (All):

Lie groups.

Representations of groups.

Physical Description:

x, 308 pages ; 24 cm.

Place of Publication:

Princeton, N.J. : Princeton University Press, 1987.

Summary:

This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs.

The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.

Notes:

Bibliography: pages 302-308.

ISBN:

0691084815 :

0691084823

OCLC:

15860326