Moment map and convex function

Abstract: The concept moment map plays a central role in the study of Hamiltonian actions of compact Lie groups $K$ on symplectic manifolds $(Z, \omega)$. In this talk, we propose a theory of moment maps coupled with an $Ad_K$-invariant convex function $f$ on $\mathfrak{t}^*$, the dual of Lie algebra of $K$, and study the structure of the stabilizer of the critical point of $f\circ\mu$ with moment map $\mu: Z \to \mathfrak{t}^*$. This work is motivated by the work of Donaldson on Ding functional, which is an example of infinite dimensional version of our setting. In particular, we obtain a natural interpretation of Tian-Zhu's generalized Futaki-invariant and Calabi-decomposition.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

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