Vol. 256, No. 2, 2012

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ISSN: 0030-8730
Quotients by actions of the derived group of a maximal unipotent subgroup

Dmitri I. Panyushev

Vol. 256 (2012), No. 2, 381–405
Abstract

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

Keywords
semisimple algebraic group, quotient, equidimensional morphism, invariant
Mathematical Subject Classification 2010
Primary: 14L30, 17B20, 22E46
Milestones
Received: 26 April 2011
Revised: 11 September 2011
Accepted: 14 September 2011
Published: 30 May 2012
Authors
Dmitri I. Panyushev
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