Enright-Shelton theory and Vogan's problem for generalized principal series / Brian D. Boe, David H. Collingwood.

Format:

Book

Author/Creator:

Boe, Brian D., 1956- author.

Collingwood, David H., author.

Series:

Memoirs of the American Mathematical Society ; Number 486.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 486

Language:

English

Subjects (All):

Semisimple Lie groups.

Representations of groups.

Physical Description:

1 online resource (122 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1993.

Language Note:

English

Summary:

This book investigates the composition series of generalized principal series representations induced from a maximal cuspidal parabolic subgroup of a real reductive Lie group. Boe and Collingwood study when such representations are multiplicity-free (Vogan's Problem #3) and the problem of describing their composition factors in closed form. The results obtained are strikingly similar to those of Enright and Shelton for highest weight modules. Connections with two different flag variety decompositions are discussed.

Contents:

""Contents""; ""Abstract""; ""1. Introduction""; ""2. Notation and Preliminaries""; ""3. Some Sp[sub(n)]R results""; ""4. Inducing from Holomorphic Discrete Series""; ""5. The SO[sub(e)](2, N) cases""; ""6. The SU(p, q) case""; ""7. The Exceptional Cases""; ""8. Loewy Length Estimates""; ""9. Appendix: Exceptional Data""; ""References""

Notes:

"March 1993. Volume 102, Number 486 (first of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0063-4