14 citations · 68 across the 14 of their papers we have counts for
14 papers
Strong duality Data of type and extended -systems
Katsuyuki Naoi
The extended -systems are a number of short exact sequences in the category of finite-dimensional modules over the quantum affine algebras of types and ,…
Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's categories in general types
Katsuyuki Naoi
We prove in full generality that the generalized quantum affine Schur-Weyl duality functor, introduced by Kang-Kashiwara-Kim, gives an equivalence between the category of finite-di…
Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types
Katsuyuki Naoi, Travis Scrimshaw
We prove that, in types , and , every Kirillov--Reshetikhin module associated with the node adjacent to the adjoint one (near adjoint node)…
Existence of Kirillov-Reshetikhin crystals of type and
Katsuyuki Naoi
In this paper we prove that every Kirillov-Reshetikhin module of type and has a crystal pseudobase (crystal base modulo signs), by applying the criterion fo…
Tensor products of Kirillov-Reshetikhin modules and fusion products
Katsuyuki Naoi
We study the classical limit of a tensor product of Kirillov-Reshetikhin modules over a quantum loop algebra, and show that it is realized from the classical limits of the tensor f…
Defining relations of fusion products and Schur positivity
Katsuyuki Naoi
In this note we give defining relations of an -module defined by the fusion product of simple -modules whose highest weights are multip…
Graded limits of minimal affinizations over the quantum loop algebra of type
Jian-Rong Li, Katsuyuki Naoi
The aim of this paper is to study the graded limits of minimal affinizations over the quantum loop algebra of type . We show that the graded limits are isomorphic to multiple…
Graded Limits of Minimal Affinizations in Type D
Katsuyuki Naoi
We study the graded limits of minimal affinizations over a quantum loop algebra of type D in the regular case. We show that the graded limits are isomorphic to multiple generalizat…
Demazure modules and graded limits of minimal affinizations
Katsuyuki Naoi
For a minimal affinization over a quantum loop algebra of type BC, we provide a character formula in terms of Demazure operators and multiplicities in terms of crystal bases. We al…
Fusion products of Kirillov-Reshetikhin modules and the X = M conjecture
Katsuyuki Naoi
In this article, we show in the ADE case that the fusion product of Kirillov-Reshetikhin modules for a current algebra, whose character is expressed in terms of fermionic forms, ca…
Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels
Katsuyuki Naoi
In this paper, we study a tensor product of perfect Kirillov-Reshetikhin crystals (KR crystals for short) whose levels are not necessarily equal. We show that, by tensoring with a…
Loewy series of Weyl modules and the Poincaré polynomials of quiver varieties
Ryosuke Kodera, Katsuyuki Naoi
We prove that a Weyl module for the current Lie algebra associated with a simple Lie algebra of type is rigid, that is, it has a unique Loewy series. Further we use this resu…
Weyl modules, Demazure modules and finite crystals for non-simply laced type
Katsuyuki Naoi
We show that every Weyl module for a current algebra has a filtration whose successive quotients are isomorphic to Demazure modules, and that the path model for a tensor product of…
Multiloop Lie algebras and the construction of extended affine Lie algebras
Katsuyuki Naoi
It is known that a multiloop Lie algebra, which constructed using multiloop realization, can be a Lie torus if the given multiloop Lie algebra satisfies several conditions, and it…