Non-Recursive Multiplicity Formulas for $A_N$ Lie Algebras

Details Non-Recursive Multiplicity Formulas for $A_N$ Lie Algebras Non-Recursive Multiplicity Formulas for $A_N$ Lie Algebras

1996-11-11

arxiv.org/abs/physics/9611008v3

Physics

Mathematical Physics

10 pages, no figures, TeX, some minor corrections in pages 3, change in e-mail address

Scientific paper

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.

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