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arXiv · 1809.03622

A Kazhdan-Lusztig algorithm for Whittaker modules

Anna Romanov
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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.

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Anna Romanov. 2019-11-19. A Kazhdan-Lusztig algorithm for Whittaker modules. https://arxiv.org/abs/1809.03622

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