arXiv subjects
Publications and source records attributed to Weideng Cui.
Inspired by the work of Rostam, we establish an explicit categorical equivalence between affine Yokonuma-Hecke algebras and quiver Hecke algebras associated to disjoint copies of quivers of (affine) type $A,$ generalizing Rouquier's categorical equivalence theorem.
Following Kashiwara's algebraic approach in one-parameter case, we construct crystal bases for two-parameter quantum algebras and for their integrable modules. We also show that the global crystal basis coincides with the canonical basis geometrically constructed by Fan and Li up to a 2-cocycle deformation.
We define Kazhdan-Lusztig bases and study asymptotic forms for affine $q$-Schur algebras following Du and McGerty. We will show that the analogues of Lusztig's conjectures for Hecke algebras with unequal parameters hold for affine $q$-Schur algebras. We will also show that the affine $q$-Schur algebra $\mathcal{S}_{q,k}^{\vartriangle}(2,2)$ over a field $k$ has finite global dimension when char $k=0$ and $1+q\neq 0.$
The modified quantized enveloping algebra $\dot{\mathbf{U}}$ has a remarkable canonical basis, which was introduced by Lusztig. In this paper, we give an explicit description of all elements of the canonical basis of $\dot{\mathbf{U}}$ for type $A_{2}$.
We show that the affine BMW algebras are affine cellular algebras.
We show that the affine Brauer algebras are affine cellular algebras in the sense of Koenig and Xi.
In this paper, we give a unified construction of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$, two-parameter Kashiwara algebras $B_{r,s}(\mathfrak{g})$, two-parameter quantized Weyl algebras $W_{r,s}(\mathfrak{g})$ and the action of $U_{r,s}(\mathfrak{g})$ on $B_{r,s}(\mathfrak{g})$ and $W_{r,s}(\mathfrak{g})$. Applying their properties to the category $\mathcal{O}(B_{r,s}(\mathfrak{g}))$, whose objects are "upper bounded" $B_{r,s}(\mathfrak{g})$-modules, We can give a conceptual proof of its semi-simplicity and the classification of simple modules in it.