Study of invariants and various structure of symplectic quotients

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540093
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Chuo University
• Principal Investigator: TAKAKURA TATSURU 中央大学, 理工学部, 教授 (30268974)
• Co-Investigator(Kenkyū-buntansha): MIYOSHI Shigeaki 中央大学, 理工学部, 教授 (60166212)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: シンプレクティック商 / 余随伴軌道 / 旗多様体 / ベクトル分割関数 / 超幾何関数 / ウェイト多様体

Outline of Final Research Achievements

First, we obtained an explicit formula for a vector partition function with possibly negative weights. As an example, for the root system of type A, we obtain an alternative proof of certain formulas for the vector partition/volume function over the `nice chamber.' They are also applied to a presentation of solutions of a certain hypergeometric system. Second, we explicitly described the special multiple weight variety of type A as a tower of projective space bundles. Consequently, the cohomology ring of this space is written down in a very simple form. As an application, we obtained a system of differential equations which characterizes the special vector volume function of type A.

Free Research Field

幾何学