Non-Recursive Multiplicity Formulas for $A_N$ Lie Algebras
Abstract
Description
It is shown that there are infinitely many formulas to calculate multiplicities of weights participating in irreducible representations of $A_N$ Lie algebras. On contrary to recursive character of Kostant and Freudenthal multiplicity formulas, they provide us systems of linear algebraic equations with N-dependent polinomial coefficients. These polinomial coefficients are in fact related with polinomials which represent eigenvalues of Casimir operators.
10 pages, no figures, TeX, some minor corrections in pages 3, change in e-mail address
10 pages, no figures, TeX, some minor corrections in pages 3, change in e-mail address