Semisymmetric polynomials and the invariant theory of matrix vector pairs
arXiv:math/9910060 · doi:10.1090/S1088-4165-01-00129-7
Abstract
In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fact, the family forms a basis of the space of semisymmetric polynomials. For two values of the parameter r, namely r=1/2 and r=1, the polynomials have a representation theoretic meaning. In general, they form the semisymmetric analogue of (shifted) Jack polynomials.
Much more detailed version (52 pages from 26). Computations for two-row diagrams are new