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Journal of Lie Theory, Vol. 10, No. 2, pp. 345-357 (2000)
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On the stability of subgroup actions on certain quasihomogeneous $G$-varieties

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Ivan Arzhantsev

Department of Mathematics

Moscow State Pedagogical University

Krasnoprudnaia 14, Moscow, Russia

ivan@arjantse.mccme.ru

**Abstract:** Let $G$ be a simple algebraic group, $U$ be a maximal unipotent subgroup of $G$, and $X$ be the affine $G$-variety corresponding to the algebra of regular functions on the homogeneous space $G/U$. We classify all subgroups $H$ of $G$ such that the restricted action $H:X$ is stable, and that $H$ is either a simple or a semisimple irreducible subgroup of $G$.

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