PIRSA:18020085

The wonderful compactication and the universal centralizer

Balibanu, A. (2018). The wonderful compactication and the universal centralizer. Perimeter Institute. https://pirsa.org/18020085

          @misc{ pirsa_PIRSA:18020085,
            doi = {10.48660/18020085},
            url = {https://pirsa.org/18020085},
            author = {Balibanu, Ana},
            keywords = {Mathematical physics},
            language = {en},
            title = {The wonderful compactication and the universal centralizer},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {feb},
            note = {PIRSA:18020085 see, \url{https://pirsa.org}}
          }

Ana Balibanu Harvard University

February 26, 2018

Talk numberPIRSA:18020085

DOI10.48660/18020085

Collection

Mathematical Physics

Talk Type Scientific Series

Subject

Mathematical physics

Abstract

Let $G$ be a complex semisimple algebraic group of adjoint type and $\overline{G}$ the wonderful compacti
cation. We show that the closure in \overline{G} of the centralizer $G^e$ of a regular nilpotent $e \in Lie(G)$ is isomorphic to the Peterson variety. We generalize this result to show that for any regular $x \in Lie(G)$ , the closure of the centralizer $G^x$ in $\overline{G}$ is isomorphic to the closure of a general $G^x$ -orbit in the flag variety. We consider the family of all such centralizer closures, which is a partial compactication of the universal centralizer. We show that it has a natural log-symplectic Poisson structure that extends the usual symplectic structure on the universal centralizer.