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Geometric crystal of type D^{(1)}_n

Algebra & Discrete Mathematics

Speaker: Taichiro Takagi, National Defense Academy, Kanagawa
Location: 693 Kerr
Start time: Thu, Mar 13 2003, 1:10PM

I will discuss properties of a birational map, which we call "tropical R", acting on products of the geometric crystals. The tropical R intertwines the actions of the geometric Kashiwara operators, like the quantum R matrix intertwines those of the generators of a quantum group. In the simplest type A case, it gives a solution of the discrete Toda equation. In a recent work with Kuniba, Okado and Yamada, I constructed the tropical R for type D case. In this talk I will explain the basic ideas of our construction mainly using simpler type A case.