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

Abstract

The Lie algebra $s{l}_2(\mathbb{C})$ 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 $s{l}_2(\mathbb{C})$ 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.

Changes made to introduction and organization of sections

References in corpus (1)

• Simple sl_{n+1}-module structures on U(h)