Study of Classical and Quantum Integrable Systems and their discretizations

K.Hasegawa研究了K.Kajiwara，M.Noumi和Y.Yamada提出的离散化Painleve方程及其对称性(Backlund变换)的量子化。特别是，他成功地构造了金宝和酒井的离散Painleve VIth方程的量子化。G.黑木研究了一般情况下保持单调变形的量子化和离散化。他成功地从装饰链和几何晶体的角度重建了长谷川对巴克伦德变换的量子化。Y.Yamada研究了二维可解格子统计模型中相关结构的热带化，得到了许多组合对应关系。对离散Painleve系统也进行了研究。得到了椭圆型和/或退化离散Painleve方程的超几何解。将该方法应用于微分情况下的哈密顿结构。池田研究了孤子方程的约化问题。他利用Fermionic Fock空间得到了Schur的Q-函数的一个组合公式。他还成功地将Schur的q-函数确定为等变上同调中的一些类，这表明在环面作用及其不动点背景下的特殊函数的研究将是卓有成效的。

K.Hasegawa studied the quantization of the discretized Painleve equation and its symmetries (Backlund transformations) proposed by K.Kajiwara, M.Noumi and Y.Yamada. Especially he succeeded to construct the quatization of the discrete Painleve VIth equation of Jimbo and Sakai.G.Kuroki studied the quantization and discretization of the monodromy preserving deformation in general. He succeeded to reconstruct Hasegawa's quantization of Bcklund transformations from the viewpoint of dressing chains and geometric crystals. Also he tried to formulate the quantized theory as the deformation of the conformal field theory under the symmetry of W-algebras.Y.Yamada studied the tropicalization of the structures relevant in the two dimensional solvable lattice statistical models, yielding many combinatorial corresspondances. Also studied are the discrete Painleve systems. Hypergeometric solutions for the elliptic and/or degenerate discrete Painleve equations are obtained. The method was applied to the Hamiltonian sturucture for the differential case.T.Ikeda studied the reductions of solitonic equations. Heused the Fermionic Fock space to obtain a combinatorial formula for Schur's Q- functions. Also he succeded to identify Schur's Q-functions as some classes in equivariant cohomologies, suggesting that the study of special functions in the setting of torus action and its fixed points will be fruitful.