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Computer Approaches to the Representations of Lie Algebras

Computer Approaches to the Representations of Lie Algebras Computer Approaches to the Representations of Lie Algebras ROBERT E . BECK Villanova University, ViUanova, Pennsylvania AND BERNARD KOLMAN Drexel University, Philadelphia, Pennsylvania ABSTRACT. This paper surveys the methods of computing the inner multiplicities of an irreducible representation of a complex simple Lie algebra. It provides a descriptive background of Lie algebra representation theory to enable the reader to follow the computations. FORTRAN programs to evaluate inner multiplicities using the Kostant and Racah formulas are described. Their features are compared and suggestions are made for combining and extending existing programs. KEY WORDS AND PHRASES: Lie algebra, Lie group, irreducible representation, inner multiplicity, weight, partition function, Weyl group, Kostant's formula, Racah's formula, Freudenthal's formula CR CATEGORIES: 3.15, 3.17, 5.39 Introduction Lie a l g e b r a s h a v e been successfully a p p l i e d to m a n y p r o b l e m s in w i d e l y diversified fields. A s a m p l i n g of such a r e a s includes differential equations, special functions, classical a n d q u a n t u m mechanics, p e http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the ACM (JACM) Association for Computing Machinery

Computer Approaches to the Representations of Lie Algebras

Journal of the ACM (JACM) , Volume 19 (4) – Oct 1, 1972

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Publisher
Association for Computing Machinery
Copyright
Copyright © 1972 by ACM Inc.
ISSN
0004-5411
DOI
10.1145/321724.321725
Publisher site
See Article on Publisher Site

Abstract

Computer Approaches to the Representations of Lie Algebras ROBERT E . BECK Villanova University, ViUanova, Pennsylvania AND BERNARD KOLMAN Drexel University, Philadelphia, Pennsylvania ABSTRACT. This paper surveys the methods of computing the inner multiplicities of an irreducible representation of a complex simple Lie algebra. It provides a descriptive background of Lie algebra representation theory to enable the reader to follow the computations. FORTRAN programs to evaluate inner multiplicities using the Kostant and Racah formulas are described. Their features are compared and suggestions are made for combining and extending existing programs. KEY WORDS AND PHRASES: Lie algebra, Lie group, irreducible representation, inner multiplicity, weight, partition function, Weyl group, Kostant's formula, Racah's formula, Freudenthal's formula CR CATEGORIES: 3.15, 3.17, 5.39 Introduction Lie a l g e b r a s h a v e been successfully a p p l i e d to m a n y p r o b l e m s in w i d e l y diversified fields. A s a m p l i n g of such a r e a s includes differential equations, special functions, classical a n d q u a n t u m mechanics, p e

Journal

Journal of the ACM (JACM)Association for Computing Machinery

Published: Oct 1, 1972

References