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arXiv · 2003.00988

The restriction of polynomial modules for the Virasoro algebra to $\mathfrak{sl}_2 ( \cc )$

Matthew Ondrus·Emilie Wiesner
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Abstract

The Lie algebra $sl_2 ( \mathbb{C} )$ may be regarded in a natural way as a subalgebra of the infinite-dimensional Virasoro Lie algebra, and this suggests there may be connections between the representation theory of the two algebras. In this paper, we explore the restriction to $sl_2 ( \mathbb{C} )$ of certain induced modules for the Virasoro algebra. Specifically, we consider Virasoro modules induced from so-called polynomial subalgebras, and we show that the restriction of these modules results in twisted versions of familiar modules such as Verma modules and Whittaker modules.

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BibTeXRIS

Matthew Ondrus, Emilie Wiesner. 2020-03-02. The restriction of polynomial modules for the Virasoro algebra to $\mathfrak{sl}_2 ( \cc )$. https://arxiv.org/abs/2003.00988

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