相关论文: Two-parameter Quantum Affine Algebra $U_{r,s}(\wid…
We introduce the two-parameter quantum affine algebra $U_{r,s}(\widehat{gl}_n)$ via the RTT realization. The Drinfeld realization is given and the type A quantum affine algebra is proved to be a special subalgebra of our extended algebra.
We obtain the basic $R$-matrix of the two-parameter Quantum group $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$ via its weight representation theory and determine its $R$-matrix with spectral parameters for the two-parameter quantum affine…
In this paper, we first review the definition of the novel quantum affine algebra \(U_{\textbf{q}}(\widehat{\mathfrak{sl}}_2)\) of type \(A_{1}^{(1)}\) given in \cite{FHZ, HZhuang}. Furthermore, by introducing \(\Omega\)-invariant…
We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras,…
Using super RS construction method and Gauss decomposition, we obtain Drinfeld's currents realization of two-parameter quantum affine superalgebra $U_{p,q}\widehat{(gl(1|1))}$ and get co-product structure for these currents.
From the theory of finite-dimensional weight modules, we get the basic braided $R$-matrix $\widehat R$ of $U_{r, s}(\mathfrak{so}_{2n+1})$. For its FRT presentation $U(\widehat R)$, we achieve two word-formation methods of quantum Lyndon…
We find the defining structures of two-parameter quantum groups $U_{r,s}(\frak g)$ corresponding to the orthogonal and the symplectic Lie algebras, which are realized as Drinfel'd doubles. We further investigate the environment conditions…
We establish an explicit correspondence between the Drinfeld current algebra presentation for the two-parameter quantum affine algebra $U_{r, s}(\mathrm{C}_n^{(1)})$ and the $R$-matrix realization \'a la Faddeev, Reshetikhin and Takhtajan.
We put forward the exact version of two-parameter generating functions with $\tau$-invariance, which allows us to give a unified and inherent definition for the Drinfeld realization of two-parameter quantum affine algebras for all the…
A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.
We obtain Drinfel'd's realization of quantum affine superalgebra $U_q\hat{(gl(1|1))}$ based on the super version of RS construction method and Gauss decomposition.
The two-parameter quantum vertex operator representation of level-one is explicitly constructed for $U_{r,s}(C^{(1)}_n)$ based on its two-parameter Drinfeld realization we give. This construction will degenerate to the one-parameter case…
In this paper, we extend the Reshetikhin-Semenov-Tian-Shansky formulation of quantum affine algebras to the two-parameter quantum affine superalgebra $U_{p, q}(\widehat{\mathfrak{gl}}(m|n))$ and obtain its Drinfeld realization. We also…
We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n. We show that these quantum groups can be realized as Drinfel'd doubles of certain Hopf subalgebras with respect…
In this article we establish explicit isomorphisms between three realizations of quantum twisted affine algebra $U_q(A_2^{(2)})$: the Drinfeld ("current") realization, the Chevalley realization and the so-called $RLL$ realization,…
In this paper, we study the two-parameter quantum group $U_{r,s}(\mathfrak sl_{\infty})$ associated to the Lie algebra $\mathfrak sl_{\infty}$ of infinite rank. We shall prove that the two-parameter quantum group $U_{r,s}(\mathfrak…
Finite dimensional irreducible modules of the two-parameter quantum enveloping algebra $U_{r,s}(\mathfrak{sl}_n)$ are explicitly constructed using the fusion procedure when $rs^{-1}$ is generic. This provides an alternative and…
We express the comultiplication of the generators in Drinfelds second realization of the quantum affine algebra U_q(sl_2^), induced by the comultiplication of the generators in the Drinfeld-Jimbo realization of U_q(sl_2^) in terms of…
We provide a deformation, $\mathfrak{f}_{\beta}$, of Lusztig algebra $\mathbf{f}$. Various quantum algebras in literatures, including half parts of two-parameter quantum algebras, quantum superalgebras, and multi-parameter quantum…
We give the defining structure of two-parameter quantum group of type G_2 defined over a field {\Bbb Q}(r,s) (with r\ne s), and prove the Drinfel'd double structure as its upper and lower triangular parts, extending an earlier result of…