D^（1）_n的几何晶体与热带R
Geometric Crystal and Tropical R for D^(1)_n
摘要：
构造了仿射李代数D^{（1）}_n在Berenstein和Kazhdan意义下的几何晶体.基于一个包含谱参数的矩阵实现，我们证明了几何晶体乘积的双有理映射热带R的唯一性和显式形式。热带R与几何Kashiwara算子可交换，满足杨-巴克斯特方程。它是减法免费的，并产生一个分段的线性公式的组合R的晶体超离散化。
英文摘要：
We construct a geometric crystal for the affine Lie algebra D^{(1)}_n in the sense of Berenstein and Kazhdan. Based on a matrix realization including a spectral parameter, we prove uniqueness and explicit form of the tropical R, the birational map that intertwines products of the geometric crystals. The tropical R commutes with geometric Kashiwara operators and satisfies the Yang-Baxter equation. It is subtraction-free and yields a piecewise linear formula of the combinatorial R for crystals upon ultradiscretization.
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