Semisymmetric polynomials and the invariant theory of matrix vector pairs
Abstract
In this paper we introduce and investigate a oneparameter 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1999
 arXiv:
 arXiv:math/9910060
 Bibcode:
 1999math.....10060K
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Combinatorics;
 Mathematics  Quantum Algebra;
 33D55;
 20G05;
 39A70;
 05E35
 EPrint:
 Much more detailed version (52 pages from 26). Computations for tworow diagrams are new