32 citations · 103 across the 12 of their papers we have counts for
12 papers
Unitriangular R-matrices of quantum affine algebras and Yangians via Theta series
Huafeng Zhang
The universal R-matrix of the quantum affine algebra associated to a finite-dimensional simple complex Lie algebra admits a Gauss decomposition into an uper unitriangular part, an…
Theta series for quantum loop algebras and Yangians
Huafeng Zhang
We introduce and study a family of power series, which we call Theta series, whose coefficients are in the tensor square of a quantum loop algebra. They arise from a coproduct fact…
Shifted Yangians and polynomial R-matrices
David Hernandez, Huafeng Zhang
We study the category O of representations over a shifted Yangian. This category has a tensor product structure and contains distinguished modules, the positive prefundamental modu…
Elliptic quantum groups and Baxter relations
Huafeng Zhang
We introduce a category O of modules over the elliptic quantum group of sl_N with well-behaved q-character theory. We construct asymptotic modules as analytic continuation of a fam…
Length-two representations of quantum affine superalgebras and Baxter operators
Huafeng Zhang
Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter T…
Baxter operators and asymptotic representations
Giovanni Felder, Huafeng Zhang
We introduce a category of representations of the elliptic quantum group associated with with well-behaved -character theory. We derive separation…
Two-parameter quantum general linear supergroups
Huafeng Zhang
The universal R-matrix of two-parameter quantum general linear supergroups is computed explicitly based on the RTT realization of Faddeev--Reshetikhin--Takhtajan.
Fundamental representations of quantum affine superalgebras and R-matrices
Huafeng Zhang
We study a certain family of finite-dimensional simple representations over quantum affine superalgebras associated to general linear Lie superalgebras, the so-called fundamental r…
Universal R-matrix of quantum affine gl(1,1)
Huafeng Zhang
The universal -matrix of the quantum affine superalgebra associated to the Lie superalgebra is realized as the Casimir element of certain Hopf pairing, base…
Asymptotic Representations of Quantum Affine Superalgebras
Huafeng Zhang
We study representations of the quantum affine superalgebra associated with a general linear Lie superalgebra. In the spirit of Hernandez-Jimbo, we construct inductive systems of K…
RTT realization of quantum affine superalgebras and tensor products
Huafeng Zhang
We use the RTT realization of the quantum affine superalgebra associated with the Lie superalgebra to study its finite-dimensional representations and their te…
Representations of Quantum Affine Superalgebras
Huafeng Zhang
We study the quantum affine superalgebra and its finite-dimensional representations. We prove a triangular decomposition and establish a system of Poincaré-Birkhoff…