Singular vectors of $N=1$ super Virasoro algebra via Uglov symmetric functions

Abstract

We give a proof of the conjecture by Belavin, Bershtein and Tarnopolsky, which claims that a bosonization of singular vectors of $N=1$ super Virasoro algebra can be identified with Uglov (Jack ${\mathfrak{gl}}_p$) symmetric functions with $p=2$.

15 pages

References in corpus (1)

• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity

Cited by in corpus (6)

• Superconformal minimal models and admissible Jack polynomials
• Admissible level $\mathfrak{osp}(1|2)$ minimal models and their relaxed highest weight modules
• The super-Virasoro singular vectors and Jack superpolynomials relationship revisited
• Singular vectors for the $W_N$ algebras
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• NSR singular vectors from Uglov polynomials