Elliptic Lie (super)algebras, affine Lie superalgebras and their quauntum groupsand their representation theories

研究了Coxeter半群（群拟）及其相关的matsumoto型定理。Yamane在与Heckenberger的合作中，受到李超代数和Nicols代数研究的启发，引入了Coxeter半群的概念。他还证明了matsumot型定理，即长度相同的Coxeter半群中的任意两个元素仅通过Coxeter（辫）关系从一个元素变换到另一个元素。Miki研究了A型量子环面代数和麦克唐纳差分算子。

Coxeter semigroups (groupoids) and an associated Matsumoto-type theorem were studied. Yamane, in a joint work with Heckenberger, intruduced a notion of the Coxeter semigroups, being inspired by research of Lie superalgebras and Nicols algebras. He also showed a Matsumot-type theorem, that is, any two elements of the Coxeter semigroups having the same length are transformed from one to the other by the Coxeter (braid) relations only. Miki studied the type A quantum toroidal algebras and Macdonald's defference operators.