Kazhdan-Lusztig Algorithm for Whittaker Modules with Arbitrary Infinitesimal Characters

Abstract

Let $\mathfrak{g}$ be a complex semisimple Lie algebra. We give a description of characters of irreducible Whittaker modules for $\mathfrak{g}$ with any infinitesimal character, along with a Kazhdan-Lusztig algorithm for computing them. This generalizes Milicic-Soergel's and Romanov's results for integral infinitesimal characters. As a special case, we recover the non-integral Kazhdan-Lusztig conjecture for Verma modules.

arXiv commentChanges in v3: Title is changed to better reflect the content of the paper. Exposition is improved, especially the introduction. Notations are also improved. Various typos are corrected. Changes in v4: corrected more typos

References in corpus (1)

• Kazhdan-Lusztig Algorithm for Whittaker Modules with Arbitrary Infinitesimal Characters

Cited by in corpus (1)

• Kazhdan-Lusztig Algorithm for Whittaker Modules with Arbitrary Infinitesimal Characters