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A Katsylo theorem for sheets of spherical conjugacy classes


Authors: Giovanna Carnovale and Francesco Esposito
Journal: Represent. Theory 19 (2015), 263-280
MSC (2010): Primary 20G15; Secondary 17B45
DOI: https://doi.org/10.1090/ert/470
Published electronically: November 2, 2015
MathSciNet review: 3417486
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Abstract: 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
Email: carnoval@math.unipd.it

Francesco Esposito
Affiliation: Dipartimento di Matematica, Torre Archimede - via Trieste 63 - 35121 Padova, Italy
Email: esposito@math.unipd.it

DOI: https://doi.org/10.1090/ert/470
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.
Article copyright: © Copyright 2015 American Mathematical Society