Stability with respect to actions of real reductive Lie groups

Leonardo Biliotti; Michela Zedda

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arXiv · 1610.05027

Stability with respect to actions of real reductive Lie groups

Leonardo Biliotti·Michela Zedda

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Abstract

We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of non-compact real reductive Lie groups on topological spaces that admit functions similar to the Kempf-Ness function. The point of this construction is that one can characterize stability, semi-stability and polystability of a point by numerical criteria, that is in terms of a function called maximal weight. We apply this setting to the actions of a real non-compact reductive Lie group G on a real compact submanifold M of a Kaehler manifold Z and to the action of G on measures of M.

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Leonardo Biliotti, Michela Zedda. 2016-10-17. Stability with respect to actions of real reductive Lie groups. https://arxiv.org/abs/1610.05027

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