Action of Coxeter groups on m-harmonic polynomials and KZ equations

Details Action of Coxeter groups on m-harmonic polynomials and KZ equations Action of Coxeter groups on m-harmonic polynomials and KZ equations

2001-08-02

arxiv.org/abs/math/0108012v2

Mathematics

Quantum Algebra

22 pages

Scientific paper

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.

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