# On reductive subgroups of reductive groups having invariants in almost all representations

@inproceedings{Tsanov2021OnRS, title={On reductive subgroups of reductive groups having invariants in almost all representations}, author={Valdemar V. Tsanov and Yana Staneva}, year={2021} }

Let G and G̃ be connected complex reductive Lie groups, G semisimple. Let Λ+ be the monoid of dominant weights for a positive root system ∆+, and let l(w) be the length of a Weyl group element w. Let Vλ denote an irreducible G-module of highest weight λ ∈ Λ+. For any closed embedding ι : G̃ ⊂ G, we consider Property (A): ∀λ ∈ Λ+,∃q ∈ N such that V G̃ qλ 6= 0. A necessary condition for (A) is for G to have no simple factors to which G projects surjectively. We show that this condition is…

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