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

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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.