Long root tori in Chevalley groups

Vavilov, N.; Semenov, A.

doi:10.1090/S1061-0022-2013-01245-3

Long root tori in Chevalley groups
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by N. A. Vavilov and A. A. Semenov
Translated by: N. A. Vavilov

St. Petersburg Math. J. 24 (2013), 387-430

DOI: https://doi.org/10.1090/S1061-0022-2013-01245-3

Published electronically: March 21, 2013

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Abstract:

In this paper we study some remarkable semisimple elements of an (extended) Chevalley group that are diagonalizable over the ground field — the ‘weight elements’. In particular, we calculate the Bruhat decomposition of microweight elements. Results of the present paper are crucial for the description of overgroups of split maximal tori in Chevalley groups.

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