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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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A Katsylo theorem for sheets of spherical conjugacy classes
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by Giovanna Carnovale and Francesco Esposito PDF
Represent. Theory 19 (2015), 263-280 Request permission


We show that, for a sheet or a Lusztig stratum $S$ containing spherical conjugacy classes in a connected reductive algebraic group $G$ over an algebraically closed field in good characteristic, the orbit space $S/G$ is isomorphic to the quotient of an affine subvariety of $G$ modulo the action of a finite abelian $2$-group. The affine subvariety is a closed subset of a Bruhat double coset and the abelian group is a finite subgroup of a maximal torus of $G$. We show that sheets of spherical conjugacy classes in a simple group are always smooth and we list which strata containing spherical classes are smooth.
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Additional Information
  • Giovanna Carnovale
  • Affiliation: Dipartimento di Matematica, Torre Archimede - via Trieste 63 - 35121 Padova, Italy
  • MR Author ID: 638877
  • Email:
  • Francesco Esposito
  • Affiliation: Dipartimento di Matematica, Torre Archimede - via Trieste 63 - 35121 Padova, Italy
  • MR Author ID: 841112
  • Email:
  • Received by editor(s): January 19, 2015
  • Received by editor(s) in revised form: September 5, 2015, and September 10, 2015
  • Published electronically: November 2, 2015
  • Additional Notes: The present work was partially supported by Progetto di Ateneo CPDA125818/12 of the University of Padova, FIRB 2012 Prospettive in Teoria di Lie and PRIN 2012 Spazi di Moduli e Teoria di Lie.
  • © Copyright 2015 American Mathematical Society
  • Journal: Represent. Theory 19 (2015), 263-280
  • MSC (2010): Primary 20G15; Secondary 17B45
  • DOI:
  • MathSciNet review: 3417486