12 citations · 59 across the 23 of their papers we have counts for
24 papers
Quasi-homomorphisms of quantum cluster algebras
Wen Chang, Min Huang, Jian-Rong Li
In this paper, we study quasi-homomorphisms of quantum cluster algebras, which are quantum analogy of quasi-homomorphisms of cluster algebras introduced by Fraser. For a quantum Gr…
Clustering Cluster Algebras with Clusters
Man-Wai Cheung, Pierre-Philippe Dechant, Yang-Hui He +3
Classification of cluster variables in cluster algebras (in particular, Grassmannian cluster algebras) is an important problem, which has direct application to computations of scat…
The amplituhedron crossing and winding numbers
Xavier Blot, Jian-Rong Li
In \cite{arkani2018unwinding}, Arkani-Hamed, Thomas and Trnka formulated two conjectural descriptions of the tree amplituhedron $\ampli$ depending on the parity of . When is…
On the simplicity of the tensor product of two simple modules of quantum affine algebras
Léa Bittmann, Jian-Rong Li
Lapid and Mínguez gave a criterion of the irreducibility of the parabolic induction , where is a ladder representation and is an arbitrary irreducible representa…
Equivariant multiplicities via representations of quantum affine algebras
Elie Casbi, Jian-Rong Li
For any simply-laced type simple Lie algebra and any height function adapted to an orientation of the Dynkin diagram of , Hernandez-Leclerc int…
Real roots in the root system
Karin Baur, Jian-Rong Li, Andrei Smolensky
Motivated by the recent advances in the categorification of the cluster structure on the coordinate rings of Grassmannians of -subspaces in -space, we investigate a particula…
Construction of Rank Indecomposable Modules in Grassmannian Cluster Categories
Karin Baur, Dusko Bogdanic, Jian-Rong Li
The category of Cohen-Macaulay modules over a quotient of a preprojective algebra provides a categorification of the cluster algebra structure on the…
Rigid Indecomposable Modules in Grassmannian Cluster Categories
Karin Baur, Dusko Bogdanic, Ana Garcia Elsener +1
The coordinate ring of the Grassmannian variety of -dimensional subspaces in has a cluster algebra structure with Plücker relations giving rise to exchange relati…
Hernandez-Leclerc modules and snake graphs
Bing Duan, Jian-Rong Li, Yan-Feng Luo
In 2010, Hernandez and Leclerc studied connections between representations of quantum affine algebras and cluster algebras. In 2019, Brito and Chari defined a family of modules ove…
Dual canonical bases for unipotent groups and base affine spaces
Jian-Rong Li
Denote by the subgroup of unipotent upper triangular matrices. In this paper, we show that the dual canonical basis of (and base affine spaces) can…
Combinatorial model for m-cluster categories in type E
Bing Duan, Lisa Lamberti, Jian-Rong Li
We revisit the geometric description of cluster categories in type E in terms of colored diagonals in a polygon and generalize it to the case of m-cluster categories. As an applica…
The 4--CB Algebra and Solvable Lattice Models
Vladimir Belavin, Doron Gepner, Jian--Rong Li +1
We study the algebras underlying solvable lattice models of the type fusion interaction round the face (IRF). We propose that the algebras are universal, depending only on the numb…
Quantum affine algebras and Grassmannians
Wen Chang, Bing Duan, Chris Fraser +1
We study the relation between quantum affine algebras of type A and Grassmannian cluster algebras. Hernandez and Leclerc described an isomorphism from the Grothendieck ring of a ce…
On cacti and crystals
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
In the present work we study actions of various groups generated by involutions on the category of integrable highest weight -mo…
Quiver mutations and Boolean reflection monoids
Bing Duan, Jian-Rong Li, Yan-Feng Luo
In 2010, Everitt and Fountain introduced the concept of reflection monoids. The Boolean reflection monoids form a family of reflection monoids (symmetric inverse semigroups are Boo…
Cluster algebras and snake modules
Bing Duan, Jian-Rong Li, Yan-Feng Luo
Snake modules introduced by Mukhin and Young form a family of modules of quantum affine algebras. The aim of this paper is to prove that the Hernandez-Leclerc conjecture about mono…
On the minimal affinizations over the quantum affine algebras of type
Xin-Yang Feng, Jian-Rong Li, Yan-Feng Luo
In this paper, we study the minimal affinizations over the quantum affine algebras of type by using the theory of cluster algebras. We show that the -characters of a large…
Primitive orthogonal idempotents of Brandt semigroup algebras
Yi Zhang, Jian-Rong Li, Xiao-Song Peng +1
A complete set of primitive orthogonal idempotents plays an important role in the representation theory of an associative algebra. In this paper, we construct a complete set of pri…
On the minimal affinizations of type
Bing Duan, Jian-Rong Li, Yan-Feng Luo
In this paper, we apply the theory of cluster algebras to study minimal affinizations for the quantum affine algebra of type . We show that the -characters of a large famil…
Graded limits of minimal affinizations over the quantum loop algebra of type
Jian-Rong Li, Katsuyuki Naoi
The aim of this paper is to study the graded limits of minimal affinizations over the quantum loop algebra of type . We show that the graded limits are isomorphic to multiple…
M-systems and Cluster algebras
Qian-Qian Zhang, Bing Duan, Jian-Rong Li +1
The aim of this paper is two-fold: (1) introduce four systems of equations called M-systems and dual M-systems of types and respectively; (2) make a connection betw…
Three-term recurrence relations of minimal affinizations of type
Li Qiao, Jian-Rong Li
Minimal affinizations form a class of modules of quantum affine algebras introduced by Chari. We introduce a system of equations satisfied by the -characters of minimal affiniza…
On the extended T-system of type
Jian-Rong Li
We continue the study of extended T-systems of quantum affine algebras. We find a sub-system of the extended T-system of the quantum affine algebra of type…
XXZ-type Bethe ansatz equations and quasi-polynomials
J. R. Li, V. Tarasov
We study solutions of the Bethe ansatz equation for the XXZ-type integrable model associated with the Lie algebra sl_N. We give a correspondence between solutions of the Bethe ansa…