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Title: Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras
Authors: Benanti, Francesca
Boumova, Silvia
Drensky, Vesselin
K. Genov, Georgi
Koev, Plamen
Keywords: Rational Symmetric Functions
MacMahon Partition Analysis
Hilbert Series
Classical Invariant Theory
Noncommutative Invariant Theory
Algebras with Polynomial Identity
Cocharacter 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
ISSN: 1310-6600
Appears in Collections:Volume 38, Number 1-3

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