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

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 ${\mathfrak{g}\mathfrak{l}}_p$) symmetric functions with $p=2$.