Symmetric and Antisymmetric Vector-valued Jack Polynomials
Combinatorics
2010-11-01 v2 Representation Theory
Abstract
Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by differential-difference ("Dunkl") operators, multiplication by coordinate functions and the group algebra. By specializing Griffeth's (arXiv:0707.0251) results for the G(r,p,n) setting, one obtains norm formulae for symmetric and antisymmetric polynomials in the standard module. Such polynomials of minimum degree have norms which involve hook-lengths and generalize the norm of the alternating polynomial.
Cite
@article{arxiv.1001.4485,
title = {Symmetric and Antisymmetric Vector-valued Jack Polynomials},
author = {Charles F. Dunkl},
journal= {arXiv preprint arXiv:1001.4485},
year = {2010}
}
Comments
22 pages, added remark about the Gordon-Stafford Theorem, corrected some typos