Singular Vectors of the Virasoro Algebra

TL;DR

This paper provides explicit formulas for singular vectors in Virasoro algebra representations, verifying their correctness and explaining the structure of embeddings among these representations.

Contribution

It introduces explicit operator product formulas for singular vectors and confirms their validity, clarifying the embedding patterns in Virasoro modules.

Findings

Explicit formulas for singular vectors are derived.

Verification confirms the formulas produce true singular vectors.

Results elucidate the embedding structure of Virasoro modules.

Abstract

We give expressions for the singular vectors in the highest weight representations of the Virasoro algebra. We verify that the expressions --- which take the form of a product of operators applied to the highest weight vector --- do indeed define singular vectors. These results explain the patterns of embeddings amongst Virasoro algebra highest weight representations.