9 papers
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…
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…
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…
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…