7 papers
Quantum Sugawara operators in
Naihuan Jing, Ming Liu, Jian Zhang
We construct Sugawara operators for the quantum affine superalgebra in an explicit form which generalizes the results given in \cite{J…
Central Elements and Determinantal Identities in the Elliptic Quantum Algebra \( \mathcal{A}_{q,p}(\widehat{\mathfrak{gl}}_N)\)
Yingjie Hu, Zheng Li, Jian Zhang
Elliptic quantum algebra is the algebraic structure characterized by the elliptic solution of the Yang-Baxter equation. In this paper, we construct a family of central elements \(…
Quantum Super Littlewood Correspondences
Naihuan Jing, Yinlong Liu, Jian Zhang
In this paper, we study the Littlewood theory associated with the quantum super immanants and supersymmetric polynomials, including both the super case and the quantum generalizati…
Quantum super Manin matrices
Naihuan Jing, Yinlong Liu, Jian Zhang
Manin matrices are quantum linear transformations of general quantum spaces. In this paper, we study the -analogue of super Manin matrices and obtain several quantum versions of…
Immanant inequalities and weight spaces
Naihuan Jing, Yinlong Liu, Jian Zhang
We first obtain a trace formula for immanants of generalized principal submatrix of any complex matrix based on any weight space for finite dimensional representations of the gener…
Quantum Littlewood correspondences
Naihuan Jing, Yinlong Liu, Jian Zhang
In the 1940s Littlewood formulated three fundamental correspondences for the immanants and Schur symmetric functions on the general linear group, which establish deep connections b…
Quantum Berezinian for quantum affine superalgebra
Naihuan Jing, Li Zheng, Jian Zhang
We introduce the quantum Berezinian for the quantum affine superalgebra and show that the coefficients of the quantum Berezinian belon…