PIRSA:17020027

Symplectic geometry related to G/U and `Sicilian theories'

APA

Ginzburg, V. (2017). Symplectic geometry related to G/U and `Sicilian theories'. Perimeter Institute. https://pirsa.org/17020027

MLA

Ginzburg, Victor. Symplectic geometry related to G/U and `Sicilian theories'. Perimeter Institute, Feb. 15, 2017, https://pirsa.org/17020027

BibTex

          @misc{ pirsa_17020027,
            doi = {10.48660/17020027},
            url = {https://pirsa.org/17020027},
            author = {Ginzburg, Victor},
            keywords = {Mathematical physics},
            language = {en},
            title = {Symplectic geometry related to G/U and {\textquoteleft}Sicilian theories{\textquoteright}},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {feb},
            note = {PIRSA:17020027 see, \url{https://pirsa.org}}
          }
          

Victor Ginzburg University of Chicago

Abstract

We construct an action of the Weyl group on the affine closure of the cotangent bundle on G/U. The construction involves Hamiltonian reduction with respect to the `universal centralizer' and an interesting Lagrangian variety, the Miura variety. A closely related construction produces symplectic manifolds which play a role in `Sicilian theories' and whose existence was conjectured by Moore and Tachikawa. Some of these constructions may be reinterpreted, via the Geometric Satake, in terms of the affine grassmannian.