Fast computation of weight multiplicities
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)].
scientific article; zbMATH DE number 4042116