40 citations · 63 across the 15 of their papers we have counts for
20 papers
Differential calculus on quantized irreducible flag manifolds
Toshiyuki Tanisaki
We give a new description of the differential calculus on the quantized irreducible flag manifold given by Heckenberger-Kolb. We also define a quantum analogue of the Dolbeault com…
The ring of differential operators on a quantized flag manifold
Toshiyuki Tanisaki
We establish some properties of the ring of differential operators on the quantized flag manifold. Especially, we give an explicit description of its localization on an affine open…
Categories of -modules on a quantized flag manifold
Toshiyuki Tanisaki
There are two approaches in defining the category of -modules on a quantized flag manifold. One is due to Lunts and Rosenberg based on the - construction of the q…
The Koszul complex and a certain induced module for a quantum group
Toshiyuki Tanisaki
We give a description of a certain induced module for a quantum group of type . Together with our previous results this gives a proof of Lusztig's conjectural multiplicity formu…
Quantized flag manifolds and non-restricted modules over quantum groups at roots of unity
Toshiyuki Tanisaki
We give a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra at the -th root of unity, w…
Differential operators on quantized flag manifolds at roots of unity III
Toshiyuki Tanisaki
We describe the cohomology of the sheaf of twisted differential operators on the quantized flag manifold at a root of unity whose order is a prime power. It follows from this and o…