Related papers: Elliptic Quantum Group U_{q,p}(B_N^{(1)}) and Vert…

Introducing an H-Hopf algebroid structure into U_{q,p}(\widedhat{sl}_2), we investigate the vertex operators of the elliptic quantum group U_{q,p}(\widedhat{sl}_2) defined as intertwining operators of infinite dimensional…

We propose a new construction of vertex operators of the elliptic quantum toroidal algebra $U_{t_1,t_2,p}(\mathfrak{gl}_{N,tor})$ by combining representations of the algebra and formulas of the elliptic stable envelopes for the…

We propose new vertex operators, both the type I and the type II dual, of the elliptic quantum toroidal algebra U_{t_1,t_2,p}(gl_{1,tor}) by combining representations of U_{t_1,t_2,p}(gl_{1,tor}) and the notions of the elliptic stable…

A realization of the elliptic quantum algebra $U_{q,p}(\widehat{sl_2})$ for any given level $k$ is constructed in terms of three free boson fields and their accompanying twisted partners. It can be viewed as the elliptic deformation of…

By using the elliptic analogue of the Drinfeld currents in the elliptic algebra U_{q,p}(\hat{sl}_N), we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group B_{q,\lambda}(\hat{sl}_N).…

After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra U_{q,p}(sl_N^), we investigate a fusion of the vertex operators of U_{q,p}(sl_N^). The basic…

We construct a realization of the elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ for any given level $k$ in terms of free boson fields and their twisted partners. It can be considered as the elliptic deformation of the Wakimoto realization…

We expose the elliptic quantum groups in the Drinfeld realization associated with both the affine Lie algebra \g and the toroidal algebra \g_tor. There the level-0 and level \not=0 representations appear in a unified way so that one can…

We extend the work of Foda et al and propose an elliptic quantum algebra $A_{q,p}(\hat {sl_n})$. Similar to the case of $A_{q,p}(\hat {sl_2})$, our presentation of the algebra is based on the relation $RLL=LLR^*$, where $R$ and $R^*$ are…

In this paper,we give the explicit formulae of vertex operators of ${U_q}(\widehat{B}_l)$ for level-one as operators on the Fock space. Meanwhile, we point out that the free field realization (by one fermionic field and $l$ bosonic fields)…

Level-one representations of the quantum affine superalgebra $U_q[\hat{gl(N|N)}]$ associated to the appropriate non-standard system of simple roots and $q$-vertex operators (intertwining operators) associated with the level-one modules are…

We investigate the structure of the elliptic algebra U_{q,p}(^sl_2) introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum affine algebra U_q(^sl_2), which are elliptic analogs…

Using our recent bosonic realization of $U_q(\widehat{sp}_{2n})$, we construct explicitly the vertex operators for the level -1/2 modules of $U_q(\widehat{sp}_{2n})$ using bosonic fields. Our method contains a detailed analysis of all the…

We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra U_{q,p}(\hat{sl}_2). The algebra U_{q,p}(\hat{sl}_2) has a constructive definition in terms of the…

We construct a realization of the L-operator satisfying the RLL-relation of the face type elliptic quantum group B_{q,lambda}(A_2^(2)). The construction is based on the elliptic analogue of the Drinfeld currents of U_q(A_2^(2)), which forms…

We construct two classes of infinitely many commuting operators associated with the elliptic quantum group $U_{q,p}(\hat{sl_N})$. We call one of them the integral of motion ${\cal G}_m$, $(m \in {\mathbb N})$ and the other the boundary…

We reformurate a central extension of Felder's elliptic quantum group in the FRST formulation as a topological algebra E_{q,p}(gl_N) over the ring of formal power series in p. We then discuss the isomorphism between E_{q,p}(gl_N) and the…

$q$-vertex operators for quantum affine algebras have played important role in the theory of solvable lattice models and the quantum Knizhnik-Zamolodchikov equation. Explicit constructions of these vertex operators for most level one…

This article presents a comprehensive study of \textit{Kirchhoff-type Critical Elliptic Equations} involving $p$-sub-Laplacian Operators on the \textit{Heisenberg Group} $\mathcal{H}_{n}$. It delves into the mathematical framework of…

Bosonized q-vertex operators related to the 4-dimensional evaluation modules of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$ are constructed for arbitrary level $k=\alpha$, where $\alpha\neq 0, -1$ is a complex parameter appearing…