Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2792

 Title: Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras Authors: Benanti, FrancescaBoumova, SilviaDrensky, VesselinK. Genov, GeorgiKoev, Plamen Keywords: Rational Symmetric FunctionsMacMahon Partition AnalysisHilbert SeriesClassical Invariant TheoryNoncommutative Invariant TheoryAlgebras with Polynomial IdentityCocharacter Sequence Issue Date: 2012 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 38, No 1-3, (2012), 137p-188p Abstract: Let K be a field of any characteristic. Let the formal power series f(x1, ..., xd) = ∑ αnx1^n1 ··· xd^nd = ∑ m(λ)Sλ(x1, ..., xd), αn, m(λ) ∈ K, be a symmetric function decomposed as a series of Schur functions. When f is a rational function whose denominator is a product of binomials of the form 1−x1^a1 ··· xd^ad, we use a classical combinatorial method of Elliott of 1903 further developed in the Ω-calculus (or Partition Analysis) of MacMahon in 1916 to compute the generating function X M(f;x1, ..., xd ) = ∑ m(λ)x1^λ1 ··· xd^λd, λ = (λ1, ..., λd). M 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. Description: 2010 Mathematics Subject Classification: 05A15, 05E05, 05E10, 13A50, 15A72, 16R10, 16R30, 20G05 URI: http://hdl.handle.net/10525/2792 ISSN: 1310-6600 Appears in Collections: Volume 38, Number 1-3

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