Explicit formula for singular vectors of the Virasoro algebra with central charge less than 1

TL;DR

This paper explicitly computes the singular vectors of the Virasoro algebra for central charges less than or equal to 1, expressing them through Jack symmetric functions with rectangular Young diagrams, providing a detailed algebraic structure.

Contribution

It provides an explicit formula for singular vectors of the Virasoro algebra at c ≤ 1, linking them to Jack symmetric functions with rectangular Young diagrams.

Findings

Infinite sequence of singular vectors for each Fock space

Singular vectors expressed via Jack symmetric functions

Explicit formulas for vectors at c ≤ 1

Abstract

We calculate explicitly the singular vectors of the Virasoro algebra with the central charge $c\leq 1$. As a result, we have an infinite sequence of the singular vectors for each Fock space with given central charge and highest weight, and all its elements can be written in terms of the Jack symmetric functions with rectangular Young diagram.