Quasiinvariants of Coxeter groups and m-harmonic polynomials

2001/05/11 by Misha Feigin, M. Feigin, Feigin, M. +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math-ph #math.MP #msc:81R12

paper · pdf · doi:10.48550/arxiv.math-ph/0105014

23 pages

arxiv created 2001/05/11 · arxiv updated 2009/11/30

Abstract

The space of m-harmonic polynomials related to a Coxeter group G and a multiplicity function m on its root system is defined as the joint kernel of the properly gauged invariant integrals of the corresponding generalised quantum Calogero-Moser problem. The relation between this space and the ring of all quantum integrals of this system (which is isomorphic to the ring of corresponding quasiinvariants) is investigated.

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• Commuting differential operators and higher-dimensional algebraic varieties

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