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

الأصل · EN

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 Iₙ⁽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).