Symmetric and Antisymmetric Vector-valued 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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2010
- DOI:
- 10.48550/arXiv.1001.4485
- arXiv:
- arXiv:1001.4485
- Bibcode:
- 2010arXiv1001.4485D
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Representation Theory;
- 05E05;
- 20C30
- E-Print:
- 22 pages, added remark about the Gordon-Stafford Theorem, corrected some typos