Browsing by Author "Böhm, Sören"

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    On Overgroups of Distinguished Unipotent Elements in Reductive Groups and Finite Groups of Lie Type
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2024) Bate, Michael; Böhm, Sören; Martin, Benjamin; Röhrle, Gerhard
    Suppose G is a simple algebraic group defined over an algebraically closed field of good characteristic p. In 2018 Korhonen showed that if H is a connected reductive subgroup of G which contains a distinguished unipotent element u of G of order p, then H is G-irreducible in the sense of Serre. We present a short and uniform proof of this result using so-called good A1 subgroups of G, introduced by Seitz. We also formulate a counterpart of Korhonen's theorem for overgroups of u which are finite groups of Lie type. Moreover, we generalize both results above by removing the restriction on the order of u under a mild condition on p depending on the rank of G, and we present an analogue of Korhonen's theorem for Lie algebras.