On the Kazhdan–Lusztig cells in type $E_8$
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Abstract:
In 1979, Kazhdan and Lusztig introduced the notion of “cells” (left, right and two-sided) for a Coxeter group $W$, a concept with numerous applications in Lie theory and around. Here, we address algorithmic aspects of this theory for finite $W$ which are important in applications, e.g., run explicitly through all left cells, determine the values of Lusztig’s $\mathbf {a}$-function, identify the characters of left cell representations. The aim is to show how type $E_8$ (the largest group of exceptional type) can be handled systematically and efficiently, too. This allows us, for the first time, to solve some open questions in this case, including Kottwitz’ conjecture on left cells and involutions.References
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Additional Information
- Meinolf Geck
- Affiliation: Fachbereich Mathematik, IAZ–Lehrstuhl für Algebra, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- MR Author ID: 272405
- Email: meinolf.geck@mathematik.uni-stuttgart.de
- Abbie Halls
- Affiliation: 21 Rubislaw Terrace Lane, Aberdeen AB10 1XF, United Kingdom
- Email: halls.abbie@gmail.com
- Received by editor(s): March 10, 2014
- Received by editor(s) in revised form: April 14, 2014
- Published electronically: May 8, 2015
- Additional Notes: This work was supported by DFG Priority Programme SPP 1489
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp. 84 (2015), 3029-3049
- MSC (2010): Primary 20C40; Secondary 20C08, 20F55
- DOI: https://doi.org/10.1090/mcom/2963
- MathSciNet review: 3378861