NSR singular vectors from Uglov polynomials

Abstract

It was conjectured in arXiv:1211.2788 that bosonization of singular vectors (in Neveu-Schwarz sector) of $\mathcal{N}=1$ super analog of the Virasoro algebra can be identified with Uglov symmetric function. In the paper we prove this conjecture. We also extend this result to the Ramond sector of $\mathcal{N}=1$ super-Virasoro algebra.

17 pages v2: many minor corrections

References in corpus (3)

• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• Virasoro Constraint for Uglov Matrix Model