%0 Journal Article
%T Generators of supersymmetric polynomials in positive characteristic
%A A. N. Grishkov
%A F. Marko
%A A. N. Zubkov
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0907.4840v1