Minimal polynomials of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in some good characteristics
https://doi.org/10.29235/1561-8323-2019-63-5-519-525
Abstract
Communicated by Academician Vyacheslav I. Yanchevskii
In a number of cases the minimal polynomials of the images of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in good characteristics are found. It is proved that if p > 5 for a group of type E8 and p > 3 for other exceptional algebraic groups, then for irreducible representations of these groups in characteristic p with large highest weights with respect to p, the degree of the minimal polynomial of the image of a unipotent element is equal to the order of this element.
Supporting agencies: The first and the second authors have been supported by the Belarusian Republican Foundation for Fundamental Research (Project no. Ф17МС-021). A substantial part of this research was done when the second author visited the Ecole Politechnique Federale de Lausanne in 2017 and 2018. She thanks the EPFL for the hospitality
About the Authors
Tatsiana S. Busel
Institute of Mathematics, National Academy of Sciences of Belarus
Belarus
Belarus
Busel Tatsiana Sergeevna - Ph. D. (Physics and Mathematics), Researcher
11, Surganov Str., 220072, Minsk
Irina D. Suprunenko
Institute of Mathematics, National Academy of Sciences of Belarus
Belarus
Belarus
Suprunenko Irina Dmitrievna - D. Sc. (Physics and Mathematics), Chief researcher.
11, Surganov Str., 220072, MinskDonna Testerman
Institute of Mathematics, Ecole Polytechnique Federale de Lausanne
Switzerland
Switzerland
Testerman Donna - Professor.
MA B3 434 (Station 8), CH-1015 Lausanne
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