Irreducible almost simple subgroups of classical algebraic groups

Abstract

Let G be a simple classical algebraic group over an algebraically closed field K of characteristic $p\ge 0$ with natural module W. Let H be a closed subgroup of G and let V be a nontrivial p-restricted irreducible tensor indecomposable rational KG-module such that the restriction of V to H is irreducible. In this paper we classify the triples (G,H,V) of this form, where $V\ne W,W^{\ast }$ and H is a disconnected almost simple positive-dimensional closed subgroup of G acting irreducibly on W. Moreover, by combining this result with earlier work, we complete the classification of the irreducible triples (G,H,V) where G is a simple algebraic group over K, and H is a maximal closed subgroup of positive dimension.

115 pages; to appear in Mem. Amer. Math. Soc

References in corpus (1)

• Symmetric powers and a problem of Kollar and Larsen