2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173289It 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 addressMathematical PhysicsAlgebraic GeometryHigh Energy Physics - Theorytext