Symmetric and Antisymmetric Vectorvalued Jack Polynomials
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 differentialdifference ("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 hooklengths and generalize the norm of the alternating polynomial.
 Publication:

arXiv eprints
 Pub Date:
 January 2010
 DOI:
 10.48550/arXiv.1001.4485
 arXiv:
 arXiv:1001.4485
 Bibcode:
 2010arXiv1001.4485D
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Representation Theory;
 05E05;
 20C30
 EPrint:
 22 pages, added remark about the GordonStafford Theorem, corrected some typos