## Toric degenerations of Gelfand-Cetlin systems and potential functions

Date: | May 21, 2008, from 15:30 |

Place: | Seminar Room at Prefab. B,
Kashiwa Campus, the University of Tokyo |

Speaker: | Kazushi Ueda (Osaka University) |

Title: | Toric degenerations of Gelfand-Cetlin systems and potential functions (joint work with Takeo Nishinou and Yuichi Nohara) |

Abstract: | Gelfand-Cetlin systems are completely integrable Hamiltonian systems on generalized flag manifolds of type A. Their momentum polytopes are called Gelfand-Cetlin polytopes, whose integral points are in bijection with Gelfand-Cetlin bases in representation theory. In the talk, we will discuss potential functions in the sense of Fukaya, Oh, Ohta and Ono for Lagrangian torus fibers in Gelfand-Cetlin systems. The basic strategy is to use Nohara's toric degenerations of Gelfand-Cetlin systems to reduce to the case of toric varieties studied by Cho and Oh. If the time allows, we will also discuss possible relationship with quantum cohomology and generalizations to Goldman systems on moduli spaces of vector bundles on curves. |