4 citations · 9 across the 14 of their papers we have counts for
14 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.
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…
PBW theory for Bosonic extensions of quantum groups
Se-jin Oh, Euiyong Park
In this paper, we develop the PBW theory for the bosonic extension $\qbA{\g}$ of a quantum group $\mathcal{U}_q(\g)$ of \emph{any} finite type. When $\g$ belongs to the class of \e…
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…
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…
Braid group action on quantum virtual Grothendieck ring through constructing presentations
Il-Seung Jang, Kyu-Hwan Lee, Se-jin Oh
As a continuation of \cite{JLO1}, we investigate the quantum virtual Grothendieck ring $\frakK_q(\g)$ associated with a finite dimensional simple Lie algebra $\g$, especially of no…
Isomorphisms among quantum Grothendieck rings and cluster algebras
Ryo Fujita, David Hernandez, Se-jin Oh +1
We establish a cluster theoretical interpretation of the isomorphisms of [F.-H.-O.-O., J. Reine Angew. Math., 2022] among quantum Grothendieck rings of representations of quantum l…
Quantization of virtual Grothendieck rings and their structure including quantum cluster algebras
Il-Seung Jang, Kyu-Hwan Lee, Se-jin Oh
The quantum Grothendieck ring of a certain category of finite-dimensional modules over a quantum loop algebra associated with a complex finite-dimensional simple Lie algebra $\math…
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…
-quantized Cartan matrix and R-matrices for cuspidal modules over quiver Hecke algebras
Masaki Kashiwara, Se-jin Oh
As every simple module of a quiver Hecke algebra appears as the image of the R-matrix defined on the convolution product of certain cuspidal modules, knowing the -invar…