Connections between the representation theory of $sl_2 ( \mathbb{C} )$ and the Virasoro algebra
arxiv(2020)
摘要
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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关键词
representation theory,$sl_2
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