8 papers · 1 filter
Monoidal seeds of the categories over quiver Hecke algebras
Masaki Kashiwara, Myungho Kim, Se-jin Oh +2
In this paper, when the quiver Hecke algebra R is symmetric, we present a new construction of quantum monoidal seeds for using the reflectio…
A Comparison of cluster algebra structures arising from -boxes and Demazure weaves
JiSun Huh, Woo-Seok Jung, Myungho Kim +1
We compare two cluster algebras related to a positive element in the braid group of finite type. One is the localized bosonic extension ${\widetilde{\mathbb{A}}}…
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…
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.
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…
Crystals and quantum twist automorphisms
Woo-Seok Jung, Euiyong Park
Let be the quantum twist automorphism for the quantum unipotent coordinate ring introduced by Kimura and Oya. In this paper, we study the qua…