A differential ideal of symmetric polynomials spanned by Jack polynomials at β=-(r-1)/(k+1)

2001/12/12 by B. Feigin, Feigin, B., M. Jimbo +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA

paper · pdf · doi:10.48550/arxiv.math/0112127

Latex, 12 pages

arxiv created 2001/12/12 · arxiv updated 2009/11/30

Abstract

For each pair of positive integers (k,r) such that k+1,r-1 are coprime, we introduce an ideal I^(k,r)_n of the ring of symmetric polynomials. The ideal I^(k,r)_n has a basis consisting of Jack polynomials with parameter β=-(r-1)/(k+1), and admits an action of a family of differential operators of Dunkl type including the positive half of the Virasoro algebra. The space I^(k,2)_n coincides with the space of all symmetric polynomials in n variables which vanish when k+1 variables are set equal. The space I_n^(2,r) coincides with the space of correlation functions of an abelian current of a vertex operator algebra related to Virasoro minimal series (3,r+2).

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