Strictly Transversal Slices to Conjugacy Classes in Algebraic Groups

Alexey Sevastyanov

doi:10.1016/j.jalgebra.2018.11.008

Strictly Transversal Slices to Conjugacy Classes in Algebraic Groups

Alexey Sevastyanov^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

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Abstract

We show that for every conjugacy class O in a connected semi-simple algebraic group G over an algebraically closed field of characteristic good for G one can find a special transversal slice Σ to the set of conjugacy classes in G such that O intersects Σ and dim O=codim Σ.

Original language	English
Pages (from-to)	309-366
Number of pages	58
Journal	Journal of Algebra
Volume	520
Early online date	27 Nov 2018
DOIs	https://doi.org/10.1016/j.jalgebra.2018.11.008
Publication status	Published - 15 Feb 2019

Keywords

Algebraic group
Transversal slice

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Accepted Manuscript
© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 297 KBLicence: CC BY-NC-ND

Alexey Sevostyanov
- School of Natural & Computing Sciences, Mathematical Science - Reader
Person: Academic

Cite this

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title = "Strictly Transversal Slices to Conjugacy Classes in Algebraic Groups",

abstract = "We show that for every conjugacy class O in a connected semi-simple algebraic group G over an algebraically closed field of characteristic good for G one can find a special transversal slice Σ to the set of conjugacy classes in G such that O intersects Σ and dim O=codim Σ.",

keywords = "Algebraic group, Transversal slice",

author = "Alexey Sevastyanov",

note = "The author is grateful to Dave Benson for his help with the MAGMA software, to Institut des Hautes {\'E}tudes Scientifiques where this work was completed, and to referees for careful checking the numeric results in Appendix B and for useful comments on the draft on this text.",

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AU - Sevastyanov, Alexey

N1 - The author is grateful to Dave Benson for his help with the MAGMA software, to Institut des Hautes Études Scientifiques where this work was completed, and to referees for careful checking the numeric results in Appendix B and for useful comments on the draft on this text.

PY - 2019/2/15

Y1 - 2019/2/15

N2 - We show that for every conjugacy class O in a connected semi-simple algebraic group G over an algebraically closed field of characteristic good for G one can find a special transversal slice Σ to the set of conjugacy classes in G such that O intersects Σ and dim O=codim Σ.

AB - We show that for every conjugacy class O in a connected semi-simple algebraic group G over an algebraically closed field of characteristic good for G one can find a special transversal slice Σ to the set of conjugacy classes in G such that O intersects Σ and dim O=codim Σ.

KW - Algebraic group

KW - Transversal slice

U2 - 10.1016/j.jalgebra.2018.11.008

DO - 10.1016/j.jalgebra.2018.11.008

M3 - Article

VL - 520

SP - 309

EP - 366

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

Strictly Transversal Slices to Conjugacy Classes in Algebraic Groups

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Alexey Sevostyanov

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