A Kazhdan-Lusztig algorithm for Whittaker modules
Abstract
We study a category of Whittaker modules over a complex semisimple Lie algebra by realizing it as a category of twisted D-modules on the associated flag variety using Beilinson-Bernstein localization. The main result of this paper is the development of a geometric algorithm for computing the composition multiplicities of standard Whittaker modules. This algorithm establishes that these multiplicities are determined by a collection of polynomials we refer to as Whittaker Kazhdan-Lusztig polynomials. In the case of trivial nilpotent character, this algorithm specializes to the usual algorithm for computing multiplicities of composition factors of Verma modules using Kazhdan-Lusztig polynomials.
Cite
@article{arxiv.1809.03622,
title = {A Kazhdan-Lusztig algorithm for Whittaker modules},
author = {Anna Romanov},
journal= {arXiv preprint arXiv:1809.03622},
year = {2019}
}
Comments
v2 54 pages; arguments in Section 4 have been modified, Lemmas 3.6, 3.7, 3.8 and Prop. 3.9 are new