arXiv: Representation Theory | 2019
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 \\cite{Soe} to study representations of the infinite dimensional Lie algebras of vector fields $W(n), S(n)$ and $H(n)$ $(n\\geq 2)$, and obtain the description of indecomposable tilting modules. The character formulas for those tilting modules are determined.