Action of Coxeter groups on m-harmonic polynomials and KZ equations
Abstract
The Matsuo-Cherednik correspondence is an isomorphism from solutions of Knizhnik-Zamolodchikov equations to eigenfunctions of generalized Calogero-Moser systems associated to Coxeter groups G and a multiplicity function m on their root systems. We apply this correspondence to the most degenerate case of zero spectral parameters. The space of eigenfunctions is then the space H_m of m-harmonic polynomials, recently introduced in math-ph/0105014. We compute the Poincare' polynomials for the space H_m and of its isotypical components corresponding to each irreducible representation of the group G. We also give an explicit formula for m-harmonic polynomials of lowest positive degree in the S_n case.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- August 2001
- DOI:
- 10.48550/arXiv.math/0108012
- arXiv:
- arXiv:math/0108012
- Bibcode:
- 2001math......8012F
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- Mathematics - Group Theory;
- 20F55 (Primary) 13A50;
- 33D80 (Secondary)
- E-Print:
- 22 pages