7 papers
Quantum cluster structures on bosonic extensions
Yingjin Bi
We construct a quantum cluster algebra structure on the standard -form of the bosonic extension algebra for every positive braid and ever…
Lusztig Parameters and Factorizations of Determinantial Modules
Yingjin Bi
We give an explicit formula for the Lusztig parameters of determinantial modules over symmetric quiver Hecke algebras. The formula applies to every Bruhat pair and every fixed redu…
Monoidal Categorification and Quantization of Braid Varieties
Yingjin Bi
Let \(G\) be a simple and simply connected algebraic group of simply-laced type. For each positive braid word \(β\), and for the complete strong duality datum attached to a \(Q\)-d…
Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type
Yingjin Bi
We study determinantial modules associated with open Richardson varieties of symmetric Kac--Moody type. For the seed obtained by the Bao--Ye--Ménard mutation procedure, we give an…
Determinantal modules over preprojective algebras and representations of Dynkin quivers
Yingjin Bi
In this paper, we study extension groups of determinantal modules over a preprojective algebra using the Auslander-Reiten translation of the quiver associated with it. More precise…
The product of simple modules over KLR algebras and quiver Grassmannians
Yingjin Bi
In this paper, we study the product of two simple modules over KLR algebras using the quiver Grassmannians for Dynkin quivers. More precisely, we establish a bridge between the Ind…
On the cohomology of quiver Grassmannians for acyclic quivers
Yingjin Bi
For an acyclic quiver, we establish a connection between the cohomology of quiver Grassmannians and the dual canonical bases of the algebra , where $U_q^-(\mat…