PIRSA:18040102

Video URL

https://pirsa.org/18040102

A Kazhdan-Lusztig algorithm for Whittaker modules

Romanov, A. (2018). A Kazhdan-Lusztig algorithm for Whittaker modules. Perimeter Institute for Theoretical Physics. https://pirsa.org/18040102

Romanov, Anna. A Kazhdan-Lusztig algorithm for Whittaker modules. Perimeter Institute for Theoretical Physics, Apr. 02, 2018, https://pirsa.org/18040102 

          @misc{ scivideos_PIRSA:18040102,
            doi = {10.48660/18040102},
            url = {https://pirsa.org/18040102},
            author = {Romanov, Anna},
            keywords = {Mathematical physics},
            language = {en},
            title = {A Kazhdan-Lusztig algorithm for Whittaker modules},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2018},
            month = {apr},
            note = {PIRSA:18040102 see, \url{https://scivideos.org/index.php/pirsa/18040102}}
          }

Anna Romanova University of Sydney

Talk numberPIRSA:18040102
DOI10.48660/18040102
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

This project examines the structure of a certain category of representations of a Lie algebra called Whittaker modules. Whittaker modules generalize highest weight modules, and the structure of the category is similar to that of Bernstein-Gelfand-Gelfand’s category O. In particular, Whittaker modules have finite length composition series and all irreducible Whittaker modules appear as quotients of standard Whittaker modules, which are generalizations of Verma modules. Using the localization theory of Beilinson-Bernstein, one obtains a beautiful geometric description of Whittaker modules as twisted sheaves of D-modules on the associated flag variety. I use this geometric setting to develop an algorithm for computing the multiplicities of irreducible Whittaker modules in the composition series of standard Whittaker modules. This algorithm establishes that the multiplicities are determined by parabolic Kazhdan-Lusztig polynomials.