Related papers: Level one representations of $U_q(G_2^{(1)})$
This paper is an extended version of our previous short letter \cite{ZG2} and is attempted to give a detailed account for the results presented in that paper. Let $U_q({\cal G}^{(1)})$ be the quantized nontwisted affine Lie algebra and…
A bosonization of the quantum affine superalgebra $U_q(\widehat{sl}(M|N))$ is presented for an arbitrary level $k \in {\bf C}$.The Wakimoto realization is given by using $\xi-\eta$ system. The screening operators that commute with…
By considering the fermionic realization of $G/H$ coset models, we show that the partition function for the $U(1)/U(1)$ model defines a Topological Quantum Field Theory and coincides with that for a 2-dimensional Abelian BF system. In the…
In this paper, we investigate finite-dimensional irreducible representations of the quantum affine general linear superalgebra $\mathrm{U}_q\big(\widehat{\mathfrak{gl}}_{m|n,\mathbf{s}}\big)$ for arbitrary 01-sequences $\mathbf{s}$, using…
In this study, we focus on the positive part $U_q^{+}$ of the quantum affine superalgebra $U_q(C(2)^{(2)})$. This algebra admits a presentation with two two generators $e_{\alpha}$ and $e_{\delta-\alpha}$, which satisfy the cubic $q$-Serre…
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…
We decompose the level-1 irreducible highest weight modules of the quantum affine algebra $U_q(\hat{sl}_n)$ with respect to the level-0 $U'_q (\hat{sl}_n)$--action defined in q-alg/9702024. The decomposition is parameterized by the skew…
We re-examine the level-one irreducible highest weight representations of the quantum affine superalgebra $U_q(\hat{sl}(2|1))$ and derive the characters and supercharacters associated with these representations. We calculate the exchange…
We investigate the characters of some finite-dimensional representations of the quantum affine algebras $U_q(\hat{g})$ using the action of the copy of $U_q(g)$ embedded in it. First, we present an efficient algorithm for computing the…
We study finite dimensional representations of the quantum affine algebra, using geometry of quiver varieties introduced by the author. As an application, we obtain character formulas expressed in terms of intersection cohomologies of…
The aim of this paper is to study the virtual classes of representation varieties of surface groups onto the rank one affine group. We perform this calculation by three different approaches: the geometric method, based on stratifying the…
We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.
The structure positive of unitary irreducible representations of the noncompact $u_q(2,1)$ quantum algebra that are related to a positive discrete series is examined. With the aid of projection operators for the $su_q(2)$ subalgebra, a…
We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it is naturally…
We construct the screening currents of the quantum superalgebra $U_q(\hat{sl}(N|1))$ for an arbitrary level $k \neq -N+1$. We show that these screening currents commute with the superalgebra modulo total difference. We propose bosonizations…
Various forms of the $q$-boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator. Both the one-component and the multicomponent $q$-bosons are discussed. As a byproduct, we obtain a new…
We study the classical and quantum $G$ extended superconformal algebras from the hamiltonian reduction of affine Lie superalgebras, with even subalgebras $G\oplus sl(2)$. At the classical level we obtain generic formulas for the Poisson…
We derive from the super RS algebra the Drinfeld basis of the twisted quantum affine superalgebra $U_q[osp(2|2)^{(2)}]$ by means of the Gauss decomposition technique. We explicitly construct a nonclassical level-one representation of…
Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $\sigma$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in…
We derive the exchange relations of the vertex operators of $U_q(A_2^{(2)})$ and show that these vertex operators give the bosonization of the Izergin-Korepin model. We give an integral expression of the correlation functions of the…