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Transformation groups 2017. Conference dedicated to Prof. Ernest B. Vinberg on the occasion of his 80th birthday
17 декабря 2017 г. 13:00, г. Москва, НИУ ВШЭ, Факультет математики (ул. Усачева, д. 6), к. 109

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The partial compactification of the universal centralizer

A. Balibanu

Harvard University, USA

Аннотация: Let $G$ be a semisimple algebraic group of adjoint type. The universal centralizer is the family of centralizers in $G$ of regular elements in $\text{Lie}(G)$, parametrized by their conjugacy classes. It has a natural symplectic structure, obtained by Hamiltonian reduction from the cotangent bundle $T^*G$. We consider a partial compactification of the universal centralizer, where each centralizer fiber is replaced by its closure inside the wonderful compactification of $G$. We show that the symplectic structure extends to a log-symplectic Poisson structure on the partial compactification, through a Hamiltonian reduction of the logarithmic cotangent bundle of the wonderful compactification.

Язык доклада: английский


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