Доклад Рио Фуджиты "Квантовая аффинная двойственность Шура-Вейля для колчанов конечного типа"

Аннотация:

For a Dynkin quiver Q (of type ADE), we consider a central completion of the convolution algebra of the equivariant K-group of a certain Steinberg type graded quiver variety. We observe that it is affine quasi-hereditary and prove that its category of finite-dimensional modules is identified with a block of Hernandez-Leclerc's monoidal category C Q of modules over the quantum loop algebra via Nakajima's homomorphism. As an application, we show that Kang-Kashiwara-Kim's generalized quantum affine Schur-Weyl duality functor gives an equivalence between the category of finite-dimensional modules of the quiver Hecke algebra associated to Q and Hernandez-Leclerc's category C Q, assuming the simpleness of poles of normalized R-matrices for type E.