9 citations · 38 across the 22 of their papers we have counts for
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Capelli identity on multiparameter quantum linear groups
Naihuan Jing, Jian Zhang
A quantum Capelli identity is given on the multiparameter quantum general linear group based on the -condition. The multiparameter quantum Pfaffian of the $(p_{ij}, u)…
Quantum Howe duality and invariant polynomials
Vyacheslav Futorny, Libor Krizka, Jian Zhang
We construct two examples of q-deformed classical Howe dual pairs (sl(2,C), sl(2,C)) and (sl(2,C), sl(n,C)). Moreover, we obtain a noncommutative version of the first fundamental t…
Gelfand-Tsetlin modules of quantum gl_n$defined by admissible sets of relations
Vyacheslav Futorny, Luis Enrique Ramirez, Jian Zhang
The purpose of this paper is to construct new families of irreducible Gelfand-Tsetlin modules for U_q(gl_n). These modules have arbitrary singularity and Gelfand-Tsetlin multiplici…
Explicit construction of irreducible modules for U_q(gl_n)
Vyacheslav Futorny, Luis Enrique Ramirez, Jian Zhang
We construct new families of U_q(gl_n)-modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object - admissible set…
Multiparameter quantum Pfaffians
Naihuan Jing, Jian Zhang
The multiparameter quantum Pfaffian of the -quantum group is introduced and studied together with the quantum determinant, and an identity relating the two invariants is gi…