论文标题
Virasoro代数的多项式模块的限制到$ \ Mathfrak {sl} _2（\ cc）$
The restriction of polynomial modules for the Virasoro algebra to $\mathfrak{sl}_2 ( \cc )$
论文作者
论文摘要
Lie代数$ SL_2（\ Mathbb {C}）$可以自然地将其视为无限维virasoro lie代数的子代数的子代数，这表明两个代数的表示理论之间可能存在联系。在本文中，我们探讨了Virasoro代数的某些诱导模块的$ sl_2（\ mathbb {c}）$的限制。具体而言，我们考虑了由所谓多项式亚域诱发的Virasoro模块，并且我们表明，这些模块的限制会导致熟悉的模块（例如Verma模块和Whittaker模块）的扭曲版本。
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.
