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

2001/08/02 by Giovanni Felder, Felder, Giovanni, Alexander P. Veselov +1
Mathematics · #20F55 (Primary) 13A50 #33D80 (Secondary) #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA) #math.AC #math.AG #math.GR #math.QA #msc:13A50 #msc:20F55 #msc:33D80

paper · pdf · doi:10.48550/arxiv.math/0108012

22 pages

arxiv created 2001/10/03 · arxiv updated 2009/11/30

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.

Related

• Quasiinvariants of Coxeter groups and m-harmonic polynomials
• Calogero-Moser eigenfunctions modulo p^s
• Harmonic locus and Calogero-Moser spaces
• Rational solutions of KZ equation, case S₄
• Lectures on quasi-invariants of Coxeter groups and the Cherednik algebra