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Lifting involutions in a Weyl group to the torus normalizer


Author: G. Lusztig
Journal: Represent. Theory 22 (2018), 27-44
MSC (2010): Primary 20G99
DOI: https://doi.org/10.1090/ert/513
Published electronically: April 24, 2018
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Abstract: Let $ N$ be the normalizer of a maximal torus $ T$ in a split reductive group over $ F_q$, and let $ w$ be an involution in the Weyl group $ N/T$. We explicitly construct a lifting $ n$ of $ w$ in $ N$ such that the image of $ n$ under the Frobenius map is equal to the inverse of $ n$.


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Additional Information

G. Lusztig
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: gyuri@math.mit.edu

DOI: https://doi.org/10.1090/ert/513
Received by editor(s): December 11, 2017
Published electronically: April 24, 2018
Additional Notes: Supported by NSF grant DMS-1566618.
Article copyright: © Copyright 2018 American Mathematical Society

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