9 citations · 38 across the 22 of their papers we have counts for
14 papers · 1 filter
Gelfand--Tsetlin bases for representations of at roots of unity
Hao Chang, Ruiying Hou, Jian Zhang
In this paper, we construct Gelfand--Tsetlin bases for representations of at roots of unity. As an application, we obtain explicit bases for certain…
Twisted q-Yangians and Sklyanin determinants
Naihuan Jing, Jian Zhang
-Yangians can be viewed both as quantum deformations of the loop algebras of upper triangular Lie algebras and deformations of the Yangian algebras. In this paper, we study the…
General Capelli-type identities
Naihuan Jing, Yinlong Liu, Jian Zhang
The classical Capelli identity is an important determinantal identity of a matrix with noncommutative entries that determines the center of the enveloping algebra of the general li…
Quantum algebra of multiparameter Manin matrices
Naihuan Jing, Yinlong Liu, Jian Zhang
Multiparametric quantum semigroups are generalization of the one-parameter general linear semigroups , where …
Minor identities for Sklyanin determinants
Naihuan Jing, Jian Zhang
We explore the invariant theory of quantum symmetric spaces of orthogonal and symplectic types by employing R-matrix techniques. Our focus involves establishing connections among t…
Dynamical quantum determinants and Pfaffians
Naihuan Jing, Jian Zhang
We introduce the dynamical quantum Pfaffian on the dynamical quantum general linear group and prove its fundamental transformation identity. Hyper quantum dynamical Pfaffian is als…
Generalized Verma modules over U_q(sl_n(C))
Vyacheslav Futorny, Libor Krizka, Jian Zhang
We construct realizations of quantum generalized Verma modules for U_q(sl_n(C)) by quan- tum differential operators. Taking the classical limit q ! 1 provides a realization of clas…
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…
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…
Quantum permanents and Hafnians via Pfaffians
Naihuan Jing, Jian Zhang
Quantum determinants and Pfaffians or permanents and Hafnians are introduced on the two parameter quantum general linear group. Fundamental identities among quantum Pf, Hf, and det…
Quantum Hyperdeterminants and Hyper-Pfaffians
Naihuan Jing, Jian Zhang
The notion of generalized quantum monoids is introduced. It is proved that the quantum coordinate ring of the monoid can be lifted to a quantum hyper-algebra, in which the quantum…
Modular Macdonald functions and Generalized Newton's identity
Tommy Wuxing Cai, Naihuan Jing, Jian Zhang
Based on a generalized Newton's identity, we construct a family of symmetric functions which deform the modular Hall-Littlewood functions. We also give a determinant formula for th…
Quantum Pfaffians and Hyper-Pfaffians
Naihuan Jing, Jian Zhang
The concept of the quantum Pfaffian is rigorously examined and refurbished using the new method of quantum exterior algebras. We derive a complete family of Plücker relations for t…