# Quotients by actions of the derived group of a maximal unipotent subgroup

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Let $U$ be a maximal unipotent subgroup of a connected semisimple group $G$ and $U$ the derived group of $U$. If $X$ is an affine $G$-variety, then the algebra of $U$-invariants, $kX^U$, is finitely generated and the quotient morphism $\pi: X \to X-U$ is well-defined. In this article, we study properties of such quotient morphisms, e.g. the property that all the fibres of $\pi$ are equidimensional. We also establish an analogue of the Hilbert-Mumford criterion for the null-cones with respect to $U$-invariants.

Autor: Dmitri I. Panyushev

Fuente: https://archive.org/