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Action of Coxeter groups on m-harmonic polynomials and KZ equations | | Giovanni Felder
; Alexander P. Veselov
; | | Date: |
2 Aug 2001 | | Subject: | Quantum Algebra; Algebraic Geometry; Group Theory; Commutative Algebra MSC-class: 20F55 (Primary) 13A50, 33D80 (Secondary) | math.QA math.AC math.AG math.GR | | Affiliation: | ETH) and Alexander P. Veselov (Loughborough University and Landau Institute | | 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. | | Source: | arXiv, math.QA/0108012 | | Services: | Forum | Review | PDF | Favorites | |
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