37 citations · 95 across the 45 of their papers we have counts for
7 papers · 1 filter
Verlinde rings and cluster algebras arising from quantum affine algebras
Chul-hee Lee, Jian-Rong Li, Euiyong Park
We formulate a positivity conjecture relating the Verlinde ring associated with an untwisted affine Lie algebra at a positive integer level and a subcategory of finite-dimensional…
Braid group actions on grassmannians and extended crystals of type
Jian-Rong Li, Euiyong Park
Let be the braid actions on infinite Grassmannian cluster algebras induced from Fraser's braid group actions. Let be the braid group actions on (quantum) Groth…
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…
Unipotent quantum coordinate ring and cominuscule prefundamental representations
Il-Seung Jang, Jae-Hoon Kwon, Euiyong Park
We continue the study of realization of the prefundamental modules , introduced by Hernandez and Jimbo, in terms of unipotent quantum coordinate rings as in [J-Kwon-…
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…