Computing with rational symmetric functions and applications to invariant theory and PI-algebras

Details Computing with rational symmetric functions and applications to invariant theory and PI-algebras Computing with rational symmetric functions and applications to invariant theory and PI-algebras

2012-01-21

arxiv.org/abs/1201.4448v1

Mathematics

Rings and Algebras

37 pages

Scientific paper

Let the formal power series f in d variables with coefficients in an arbitrary field be a symmetric function decomposed as a series of Schur functions, and let f be a rational function whose denominator is a product of binomials of the form (1 - monomial). We use a classical combinatorial method of Elliott of 1903 further developed in the Partition Analysis of MacMahon in 1916 to compute the generating function of the multiplicities (i.e., the coefficients) of the Schur functions in the expression of f. It is a rational function with denominator of a similar form as f. We apply the method to several problems on symmetric algebras, as well as problems in classical invariant theory, algebras with polynomial identities, and noncommutative invariant theory.

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