Cohomology of Deligne-Lusztig varieties for unipotent blocks of $\mathrm {GL}_n(q)$
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- by Olivier Dudas
- Represent. Theory 17 (2013), 647-662
- DOI: https://doi.org/10.1090/S1088-4165-2013-00446-6
- Published electronically: December 10, 2013
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Abstract:
We study the cohomology of parabolic Deligne-Lusztig varieties associated to unipotent blocks of $\mathrm {GL}_n(q)$. We show that the geometric version of Broué’s conjecture over $\overline {\mathbb {Q}}_\ell$, together with Craven’s formula, holds for any unipotent block whenever it holds for the principal $\Phi _1$-block.References
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Bibliographic Information
- Olivier Dudas
- Affiliation: Université Denis Diderot - Paris 7, UFR de Mathématiques, Institut de Mathématiques de Jussieu, Case 7012, 75205 Paris Cedex 13, France
- MR Author ID: 883805
- Email: dudas@math.jussieu.fr
- Received by editor(s): January 16, 2013
- Received by editor(s) in revised form: July 10, 2013
- Published electronically: December 10, 2013
- Additional Notes: The author was supported by the EPSRC, Project No EP/H026568/1 and by Magdalen College, Oxford.
- © Copyright 2013 American Mathematical Society
- Journal: Represent. Theory 17 (2013), 647-662
- MSC (2010): Primary 20C33
- DOI: https://doi.org/10.1090/S1088-4165-2013-00446-6
- MathSciNet review: 3139556