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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 |
Description
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.