Related papers: Drinfeld basis for string-inspired Baxter operator…
The Lax operator of the Gaudin type models is a 1-form on the classical level. In virtue of the quantization scheme proposed in [Talalaev04] (hep-th/0404153) it is natural to treat the quantum Lax operator as a connection; this connection…
The Drinfled realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization…
The connection between the R-matrix realization and Drinfeld's realization of the quantum loop algebra $U_q(D^{(2)}_n)$ is considered using the Gaussian decomposition approach proposed by J. Ding and I. B. Frenkel. Our main result is a…
Two universal spectral parameter-dependent Lax operators are presented in terms of the elements of the Drinfeld double $D(D_3)$ of the dihedral group $D_3$. Applying representations of $D(D_3)$ to these yields matrix solutions of the…
Surprising links between the deformation of 2D quantum field theories induced by the composite $\textrm{T} \bar{\textrm{T}}$ operator, effective string models and the $AdS/$CFT correspondence, have recently emerged. The purpose of this…
For the current realization of the quantum affine algebras, Drinfeld gave a simple comultiplication of the quantum current operators. With this comultiplication, we study the related vertex operators for the case of $U_q(\hgtsl_n)$ and give…
Utilizing the multiplicative formula of universal R matrix, the correspondence between the L operators and Drinfeld's generators is explicitly calculated for quantum group U_q(g) with g=A_l^{(1)}, B_l^{(1)}, C_l^{(1)}, D_l^{(1)}.
In this paper, we extend the Drinfeld current realization of quantum affine algebras $U_q(\hat {\gg})$ and of the Yangians in several directions: we construct current operators for non-simple roots of ${\gg}$, define a new braid group…
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we prove that, for the integrable modules of $U_q(\hat {\frak sl}(2))$…
We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…
We give a simplified description of quantum affine algebras in their loop presentation. This description is related to Drinfeld's new realization via halves of vertex operators. We also define an idempotent version of the quantum affine…
The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…
Drinfeld realisations are constructed for the quantum affine superalgebras of the series ${\rm\mathfrak{osp}}(1|2n)^{(1)}$,${\rm\mathfrak{sl}}(1|2n)^{(2)}$ and ${\rm\mathfrak{osp}}(2|2n)^{(2)}$. By using the realisations, we develop vertex…
We obtain Drinfeld second realization of the quantum affine superalgebras associated with the affine Lie superalgebra $D^{(1)}(2,1;x)$. Our results are analogous to those obtained by Beck for the quantum affine algebras. Beck's analysis…
We present a family of novel Lax operators corresponding to representations of the RTT-realisation of the Yangian associated with $D$-type Lie algebras. These Lax operators are of oscillator type, i.e. one space of the operators is…
We present a formal algebraic language to deal with quantum deformations of Lie-Rinehart algebras - or Lie algebroids, in a geometrical setting. In particular, extending the ice-breaking ideas introduced by Xu in [Ping Xu, "Quantum…
The paper is the sequel to q-alg/9704011. We extend the Drinfeld-Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic deformation of the Lie bialgebra…
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…
The $\alpha$-Bernstein operators were initially introduced in the paper by Chen, X., Tan, J., Liu, Z., Xie, J. (2017) titled "Approximation of Functions by a New Family of Generalized Bernstein Operators" (Journal of Mathematical Analysis…
We study the possibility to establish $L$-operator's formalism by Faddeev-Reshetikhin-Takhtajan-Semenov-Tian-Shansky (FRST) for quantized current algebras, that is, for quantum affine algebras in the ''new realization '' by V. Drinfeld with…