12 citations · 12 across the 10 of their papers we have counts for
10 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…
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.
Crystal Structure of Localized Quantum Unipotent Coordinate Category
Masaki Kashiwara, Toshiki Nakashima
A localized quantum unipotent coordinate category associated with a Weyl group element is a rigid monoidal category which is obtained by applying th…
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…
On the irregular Riemann-Hilbert correspondence
Andrea D'Agnolo, Masaki Kashiwara
The original Riemann-Hilbert problem asks to find a Fuchsian ordinary differential equation with prescribed singularities and monodromy in the complex line. In the early 1980's Kas…
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…
Quantized Affine Algebras and Crystals with Head
Seok-Jin Kang, Masaki Kashiwara
Motivated by the work of Nakayashiki on the inhomogeneous vertex models of 6-vertex type, we introduce the notion of crystals with head. We show that the tensor product of the high…