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

Balibanu, Ana. The wonderful compactication and the universal centralizer. Perimeter Institute, Feb. 26, 2018, 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

DOI 10.48660/18020085
Collection
Talk Type Scientific Series
Subject

Abstract

Let Gbe 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^eof 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^xin \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.