Semisymmetric polynomials and the invariant theory of matrix vector pairs

Details Semisymmetric polynomials and the invariant theory of matrix vector pairs Semisymmetric polynomials and the invariant theory of matrix vector pairs

1999-10-12

arxiv.org/abs/math/9910060v2

Represent. Theory 5 (2001), 224-266

Mathematics

Representation Theory

Much more detailed version (52 pages from 26). Computations for two-row diagrams are new

Scientific paper

10.1090/S1088-4165-01-00129-7

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.

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