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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Lifting involutions in a Weyl group to the torus normalizer
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by G. Lusztig PDF
Represent. Theory 22 (2018), 27-44 Request permission


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
  • Email:
  • Received by editor(s): December 11, 2017
  • Published electronically: April 24, 2018
  • Additional Notes: Supported by NSF grant DMS-1566618.
  • © Copyright 2018 American Mathematical Society
  • Journal: Represent. Theory 22 (2018), 27-44
  • MSC (2010): Primary 20G99
  • DOI:
  • MathSciNet review: 3789878