5 papers · 1 filter
Plabic promotions beyond cluster: quantum cluster structures and the dual canonical basis
Jian-Rong Li, Michael Oren Perlstein, Ran J. Tessler
Plabic tangles define geometric promotion maps between configurations and, after choosing a lift, between Grassmannians. The main conjecture in \cite{Tangles} is that when the tang…
Langlands branching rule for type B snake modules
Jingmin Guo, Jian-Rong Li, Keyu Wang
We prove that each snake module of the quantum Kac-Moody algebra of type admits a Langlands dual representation, as conjectured by Frenkel and Hernandez (Lett. Math. Ph…
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…
A correspondence between additive and monoidal categorifications with application to Grassmannian cluster categories
Karin Baur, Changjian Fu, Jian-rong Li
Building on work of Derksen-Fei and Plamondon, we formulate a conjectural correspondence between additive and monoidal categorifications of cluster algebras, which reveals a new co…