The Category $\mathcal{O}$ for Lie algebras of vector fields (I): Tilting modules and character formulas

Abstract

In this article, we exploit the theory of graded module category with semi-infinite character developed by Soergel in [13] to study representations of the infinite dimensional Lie algebras of vector fields W (n), S(n) and H(n) (n ≥ 2), and obtain the description of indecomposable tilting modules. The character formulas for those tilting modules are determined.