A new family of irreducible subgroups of the orthogonal algebraic groups

Cavallin, Mikaël; Testerman, Donna

doi:10.1090/btran/28

A new family of irreducible subgroups of the orthogonal algebraic groups
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Trans. Amer. Math. Soc. Ser. B 6 (2019), 45-79

Abstract:

Let $n\geq 3,$ and let $Y$ be a simply connected, simple algebraic group of type $D_{n+1}$ over an algebraically closed field $K.$ Also let $X$ be the subgroup of type $B_n$ of $Y,$ embedded in the usual way. In this paper, we correct an error in a proof of a theorem of Seitz (Mem. Amer. Math. Soc. 67 (1987), no. 365), resulting in the discovery of a new family of triples $(X,Y,V),$ where $V$ denotes a finite-dimensional, irreducible, rational $KY$-module, on which $X$ acts irreducibly. We go on to investigate the impact of the existence of the new examples on the classification of the maximal closed connected subgroups of the classical algebraic groups.

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