NSR singular vectors from Uglov polynomials

TL;DR

This paper proves a conjecture that singular vectors in the Neveu-Schwarz sector of the super-Virasoro algebra can be represented by Uglov symmetric functions and extends this to the Ramond sector.

Contribution

It establishes a new link between super-Virasoro singular vectors and Uglov symmetric functions, confirming and extending previous conjectures.

Findings

Proved the conjecture for the Neveu-Schwarz sector.

Extended the result to the Ramond sector.

Established a new algebraic-combinatorial correspondence.

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.