8 papers
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…
Grassmannian tree webs and cluster variables
Jian-Rong Li, Chenglu Wang, Lauren Williams
Homogeneous coordinate rings of Grassmannians are among the most fundamental instances of cluster algebras arising in ``nature.'' Despite their importance, however, the cluster var…
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…
From dual canonical bases to positroidal subdivisions
Jian-Rong Li, Ayush Kumar Tewari
The Grassmannian cluster algebra admits a distinguished basis known as the dual canonical basis, whose elements correspond to rectangular semi-standar…
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…
Cluster structures on spinor helicity and momentum twistor varieties
Lara Bossinger, Jian-Rong Li
We study the homogeneous coordinate rings of partial flag varieties and Grassmannians in their Plücker embeddings and exhibit an embedding of the former into the latter. Both rings…