Fast computation of weight multiplicities
type: Item
instance of: scholarly article
title: Fast computation of weight multiplicities
zbMATH Open document ID: 0639.17001
DOI: 10.1016/S0747-7171(86)80003-7
author: Murray R. Bremner
published in: Journal of Symbolic Computation
publication date: 1986-01-01T00:00:00Z
review text: This paper discusses a Pascal implementation of a fast recursion formula for multiplicities of dominant weights in finite-dimensional irreducible modules for simple complex Lie algebras. The program, developed on the CDC Cyber 835, computes the dominant weights and multiplicities, based on an algorithm, described by \textit{R. V. Moody} and \textit{J. Patera} [Bull. Am. Math. Soc., New Ser. 7, 237-242 (1982; Zbl 0494.17005)]. An example is given of the program's execution with 58 dominant weights and multiplicities of an \(E_ 8\)-module of dimension \(3.191.795.712.000,\) determined in under 13 seconds. One can ask, whether another (improved?) programming could have been achieved, if the author had been acquainted with \textit{H. Freudenthal}'s paper [L'avantage de l'usage de bases symétriques pour des calculs dans les algèbres de Lie simples, Bull. Soc. Math. Belg., Sér. A 38, 201- 208 (1986; Zbl 0628.17004)].
Mathematics Subject Classification ID: 17-04
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 4042116
zbMATH Keywords: Pascal implementation
zbMATH Keywords: fast recursion formula
zbMATH Keywords: multiplicities of dominant weights
zbMATH Keywords: irreducible modules
zbMATH Keywords: simple complex Lie algebras
reviewed by: Arie Hendrik Boers
describes a project that uses: FREUD
describes a project that uses: liealgebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4042116