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Representation Theory

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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
Published electronically: April 24, 2018
MathSciNet review: 3789878
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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
MR Author ID: 117100

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