A differential ideal of symmetric polynomials spanned by Jack polynomials at $\beta=-(r-1)/(k+1)$
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 $\beta=-(r-1)/(k+1)$, 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).
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- December 2001
- DOI:
- 10.48550/arXiv.math/0112127
- arXiv:
- arXiv:math/0112127
- Bibcode:
- 2001math.....12127F
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Combinatorics
- E-Print:
- Latex, 12 pages