6 papers
The Knot Invariant Associated to Two-Parameter Quantum Algebras II
Zhaobing Fan, Tianhao Zhu
Fan, Ma, and Xing constructed oriented-tangle invariants from finite-type two-parameter quantum algebras. In this paper, we construct an explicit parameter-transport comparison bet…
Quantum Borcherds-Bozec Superalgebras
Zhaobing Fan, Jiaqi Huang
We introduce quantum Borcherds-Bozec superalgebras. We present and prove various results of the quantum superalgebras including a bilinear form, higher Serre relation, quasi-R-matr…
Perfect basis theory for quantum Borcherds-Bozec algebras
Zhaobing Fan, Shaolong Han, Seok-Jin Kang +1
In this paper, we develop the perfect basis theory for quantum Borcherds-Bozec algebras and their irreducible highest weight modules . We show that the l…
Geometric Approach to Mirabolic Schur-Weyl Duality of Type A
Zhaobing Fan, Zhicheng Zhang, Haitao Ma
We commence by constructing the mirabolic quantum Schur algebra, utilizing the convolution algebra defined on the variety of triples of two -step partial flags and a vector. Sub…
A new Young wall realization of and
Zhaobing Fan, Shaolong Han, Seok-Jin Kang +1
Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal for the quantum affine algebras of types , $D^…
Highest weight modules over Borcherds-Bozec superalgebras and their character formula
Zhaobing Fan, Jiaqi Huang, Seok-Jin Kang +1
We present and prove the Weyl-Kac type character formula for the irreducible highest weight modules over Borcherds-Bozec superalgebras with dominant integral highest weights.