T.Tanisaki是国际知名数学家，主要研究李代数、代数群、量子群及表示理论。
I will give an account of my result on Lusztig's conjectural multiplicity formula for the modules over the De Concini-Kac type quantized enveloping algebras at roots of unity. In the first half I will give an account of some standard facts on the representation theory of the De Concini-Kac type quantized enveloping algebras at roots of unity. In the second half I will explain how we can use $D$-modules on the quantized flag manifolds in the representation theory of the quantized enveloping algebras.
