A differential ideal of symmetric polynomials spanned by Jack polynomials at $\beta=(r1)/(k+1)$
Abstract
For each pair of positive integers (k,r) such that k+1,r1 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 $\beta=(r1)/(k+1)$, 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).
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2001
 DOI:
 10.48550/arXiv.math/0112127
 arXiv:
 arXiv:math/0112127
 Bibcode:
 2001math.....12127F
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Combinatorics
 EPrint:
 Latex, 12 pages