58 citations · 298 across the 43 of their papers we have counts for
43 papers
Monoidal seeds of the categories over quiver Hecke algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
In this paper, when the quiver Hecke algebra R is symmetric, we present a new construction of quantum monoidal seeds for using the reflectio…
Newton--Okounkov bodies of partial flag varieties via cluster algebras
Yunhyung Cho, Myungho Kim, Yoosik Kim +1
We construct Newton--Okounkov polytopes of Schubert varieties in partial flag varieties of arbitrary type using the cluster structure on a unipotent cell. When the governing cluste…
Faithful action of braid group on bosonic extensions
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
The braid group action on the bosonic extension of the quantum group has been introduced in recent works, and it can be regarded as a generalization of Lusztig's symmetries on the…
Monoidal categorification and quantum affine algebras III
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
Let be an arbitrary quantum affine algebra of either untwisted or twisted type, and let be its Hernandez-Leclerc category. We de…
Reflection functors on quiver Hecke algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
We construct the reflection functors for quiver Hecke algebras of an arbitrary symmetrizable Kac-Moody type. These reflection functors categorify Lusztig's braid symmetries.
Exchange matrices of I-boxes
Masaki Kashiwara, Myungho Kim
Admissible chains of i-boxes are important combinatorial tools in the monoidal categorification of cluster algebras, as they provide seeds of the cluster algebra. In this paper, we…
Braid symmetries on bosonic extensions
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
We introduce a family of automorphisms on the bosonic extension of arbitrary type and show that they satisfy the braid relations. They preserve the global basis and the crystal bas…
Global bases for Bosonic extensions of quantum unipotent coordinate rings
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
In the paper, we establish the global basis theory for the bosonic extension associated with an arbitrary generalized Cartan matrix. When $\widehat{\mathcal…
Cluster algebras and monotone Lagrangian tori
Yunhyung Cho, Myungho Kim, Yoosik Kim +1
Motivated by the construction of Newton--Okounkov bodies and toric degenerations via cluster algebras in [GHKK18, FO25], we consider a family of Newton--Okounkov polytopes of a com…
Localizations for quiver Hecke algebras III
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
Let be a quiver Hecke algebra, and let be the category of finite-dimensional graded -module categorifying a -deformation of the doubly-invariant algeb…
Modified Ariki-Koike algebra and Yokounuma-Hecke like relations
Myungho Kim, SungSoon Kim
We find new presentations of the modified Ariki-Koike algebra (known also as Shoji's algebra) over an integral domain associated with a set of parameters $q,…
Laurent family of simple modules over quiver Hecke algebra
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
We introduce the notions of quasi-Laurent and Laurent families of simple modules over quiver Hecke algebras of arbitrary symmetrizable types. We prove that such a family plays a si…
Affinizations, R-matrices and reflection functors
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
In this paper we establish affinizations and R-matrices in the language of pro-objects, and as an application, we construct reflection functors over the localizations of quiver Hec…
Localizations for quiver Hecke algebras II
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
We prove that the localization of the monoidal category is rigid, and the category admits a localization via a real commuting family of central…
Monoidal categorification and quantum affine algebras II
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
We introduce a new family of real simple modules over the quantum affine algebras, called the affine determinantial modules, which contains the Kirillov-Reshetikhin (KR)-modules as…
PBW theory for quantum affine algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
Let be a quantum affine algebra of arbitrary type and let be Hernandez-Leclerc's category. We can associate the quantum affine Sch…
Polynomial invariants on matrices and partition, Brauer algebra
Myungho Kim, Doyun Koo
We identify the dimension of the centralizer of the symmetric group in the partition algebra and in the Brauer algebra with t…
Categories over quantum affine algebras and monoidal categorification
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
Let be a quantum affine algebra of untwisted affine type, and the Hernandez-Leclerc category of finite-dimensional $U_q'(\…
PBW theoretic approach to the module category of quantum affine algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
Let be a quantum affine algebra of untwisted affine ADE type and let be Hernandez-Leclerc's category. For a duality datum $\math…
Braid group action on the module category of quantum affine algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
Let be a simple Lie algebra of type ADE and let be the corresponding untwisted quantum affine algebra. We show that there exists an action of…
Simply-laced root systems arising from quantum affine algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
Let be a quantum affine algebra with an indeterminate and let be the category of finite-dimensional integrable $U_q'(\mathfrak…
Monoidal categorification and quantum affine algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
We introduce and investigate new invariants on the pair of modules and over quantum affine algebras by analyzing their associated R-matrices. From new…
Cluster algebra structures on module categories over quantum affine algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
We study monoidal categorifications of certain monoidal subcategories of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures c…
Localizations for quiver Hecke algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +1
We provide the localization procedure for monoidal categories by a real commuting family of braiders. For an element of the Weyl group, is a subcategory of modu…