Symmetric and Antisymmetric Vector-valued Jack Polynomials

Details Symmetric and Antisymmetric Vector-valued Jack Polynomials Symmetric and Antisymmetric Vector-valued Jack Polynomials

2010-01-25

arxiv.org/abs/1001.4485v2

Sem. Lothar. Combin. B64a (2010), 31 pp

Mathematics

Combinatorics

22 pages, added remark about the Gordon-Stafford Theorem, corrected some typos

Scientific paper

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.

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