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On the Kazhdan-Lusztig cells in type $ E_8$


Authors: Meinolf Geck and Abbie Halls
Journal: Math. Comp. 84 (2015), 3029-3049
MSC (2010): Primary 20C40; Secondary 20C08, 20F55
DOI: https://doi.org/10.1090/mcom/2963
Published electronically: May 8, 2015
MathSciNet review: 3378861
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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.


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Additional Information

Meinolf Geck
Affiliation: Fachbereich Mathematik, IAZ–Lehrstuhl für Algebra, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Email: meinolf.geck@mathematik.uni-stuttgart.de

Abbie Halls
Affiliation: 21 Rubislaw Terrace Lane, Aberdeen AB10 1XF, United Kingdom
Email: halls.abbie@gmail.com

DOI: https://doi.org/10.1090/mcom/2963
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
Article copyright: © Copyright 2015 American Mathematical Society