Explicit expressions for Virasoro singular vectors

Gérard M T Watts

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arXiv · 2412.07505

Explicit expressions for Virasoro singular vectors

Gérard M T Watts

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Abstract

We present two explicit expressions for generic singular vectors of type $(r,s)$ of the Virasoro algebra. These results follow from the paper of Bauer et al which presented recursive methods to construct the vectors. The expressions presented here generalise the results of Benoit-Saint Aubin for the type $(1,s)$ singular vectors in two different ways: the first simply solves the recursion through the use of partitions; the second gives explicit formulae for the coefficients in a particular expansion. A Mathematica notebook is available which implements the formulae.

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Gérard M T Watts. 2024-12-10. Explicit expressions for Virasoro singular vectors. https://arxiv.org/abs/2412.07505

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