Generators of supersymmetric polynomials in positive characteristic

2009/07/28 by Grishkov, A. N., Marko, F., Zubkov, A. N.
#16W22 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0907.4840

Abstract

Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie supergalgebra gl(m|n) and a related algebra A_s of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A_s was investigated earlier by Stembridge who called the elements of A_s supersymmetric polynomials and determined generators of A_s. The case of positive characteristic p has been recently investigated by La Scala and Zubkov. They formulated two conjectures describing generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m|n) and generators of A_s, respectively. In the present paper we prove both conjectures.

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