A sharp upper bound for the size of Lusztig series

Christine Bessenrodt 1  and Alexandre Zalesski 2
  • 1 Institute for Algebra, Number Theory and Discrete Mathematics, Leibniz University Hannover, Faculty of Mathematics and Physics, Hannover, Germany
  • 2 Department of Physics, Mathematics and Informatics, National Academy of Sciences of Belarus, 66 Nezalejnasti prospekt, 220072, Minsk, Belarus
Christine Bessenrodt
  • Corresponding author
  • Institute for Algebra, Number Theory and Discrete Mathematics, Faculty of Mathematics and Physics, Leibniz University Hannover, Welfengarten 1, 30167, Hannover, Germany
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and Alexandre Zalesski
  • Department of Physics, Mathematics and Informatics, National Academy of Sciences of Belarus, 66 Nezalejnasti prospekt, 220072, Minsk, Belarus
  • Email
  • Search for other articles:
  • degruyter.comGoogle Scholar

Abstract

The paper is concerned with the character theory of finite groups of Lie type. The irreducible characters of a group 𝐺 of Lie type are partitioned in Lusztig series. We provide a simple formula for an upper bound of the maximal size of a Lusztig series for classical groups with connected center; this is expressed for each group 𝐺 in terms of its Lie rank and defining characteristic. When 𝐺 is specified as G(q) and 𝑞 is large enough, we determine explicitly the maximum of the sizes of the Lusztig series of 𝐺.

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The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.

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