| Budget Amount *help |
¥3,730,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Research Abstract |
I have proved that the Gelfand-Cetlin system, a completely integrable system on a flag manifold of type A, can be deformed into a toric moment map on a toric variety (this is a joint work with T. Nishinou and K. Ueda). As an application we computed the potential functions of the Lagrangian torus fibers of the Gelfand-Cetlin system, and showed that it coincides with the superpotential of the Landau-Ginzburg mirror of the flag manifold.
It is known that toric degenerations of a Grassmannian of two-planes in a complex vector space are classified by certain trees. For each such tree I have constructed a completely integrable system on the Grassmannian, and proved that it can be deformed into a toric moment map under the corresponding toric degeneration. This result implies that completely integrable systems on a polygon space constructed by Kapovich and Millson also admit deformations into toric moment maps. I have also studied a relation between Kapovich-Milson's integrable systems and Goldman's integrable systems on a moduli space of parabolic bundles of rank 2 on a projective line.
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