Research on representation theory of algebraic groups and quantum groups via algebraic analysis

Qyabtyn griyos是代数群的q-变形。当参数q不是1的根时，它的表示理论是很好理解的;然而，当q是1的根时，仍然存在一些基本问题，如不可约模的分类尚未解决。首席研究员谷崎用D-模的方法对此进行了研究，并得到了一些结果，如某些微分算子环的Azumaya性质。研究者金田研究了正特征微分算子环，并在正特征代数群的表示理论方面取得了进展。

Qyabtyn griyos are q-deformations of algebraic groups. When the parameter q is not a root of 1, its representation theory is well unerstood ; however, when q is a root of 1, there still remain fundamental problems such as classification of irreducible modules which are not yet solved. The head investigator Tanisaki made research on it using the method of D-modules, and obtained several results like the Azumaya property of certain rings of differential operators. The investigator Kaneda investigated the ring of differential operators in positive characteristics, and made progress in the representation theory of algebraic groups in positive characteristics.