Non-Recursive Multiplicity Formulas for A_N Lie Algebras

1996/11/11 by Hasan R. Karadayi, H. R. Karadayi, Karadayi, H. R.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #alg-geom #hep-th #math-ph #math.AG #math.MP

paper · pdf · doi:10.48550/arxiv.physics/9611008

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

openalex publication_date 1996/11/11 · arxiv created 1997/01/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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