Stability in modules for classical lie algebras : a constructive approach / G. M. Benkart, D. J. Britten, and F. W. Lemire.

Format:

Book

Author/Creator:

Benkart, Georgia, 1949- author.

Britten, D. J. (Daniel J.), 1944- author.

Lemire, F. W. (Frank W.), 1942- author.

Series:

Memoirs of the American Mathematical Society ; Number 430.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 430

Language:

English

Subjects (All):

Lie algebras.

Representations of algebras.

Modules (Algebra).

Partitions (Mathematics).

Semisimple Lie groups.

Physical Description:

1 online resource (177 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1990.

Language Note:

English

Summary:

During the last century, mathematicians and physicists alike have studied extensively the finite dimensional irreducible representations of complex classical Lie algebras. These studies have led to numerous formulas for computing the dimensions, weights, weight multiplicities, and tensor products of the representations. The dependence of these quantities on the rank of the Lie algebra has been revealed in recent investigations using Schur functions and characters.

Contents:

Intro

Table of Contents

Introduction

1. Preliminaries

2. The Tensor Product Realization

3. The Dominant Weights of ⊗[sup(m)]V(ω[sub(1)],X[sub(r)])

4. The Dominant Weights of V(λ, X[sub(r)])

5. Dimensions and Polynomials

6. Stability of g[sub(r)](⊗[sup(M')]V(ω,X[sub(r)])⊗g[sup(r')](⊗[sup(M")]V(ω,X[sub(r)])

7. Stability of V(λ, X[sub(r)]) ⊗V(λ', X[sub(r)])

8. Multiplicities of the Dominant Weights of V(λ, X[sub(r)])

9. Algorithms and Examples

Notation

References.

Notes:

"May 1990, Volume 85, number 430, (end of volume)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0853-8