Lifting involutions in a Weyl group to the torus normalizer

Lusztig, G.

doi:10.1090/ert/513

Lifting involutions in a Weyl group to the torus normalizer
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by G. Lusztig

Represent. Theory 22 (2018), 27-44

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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