相关论文: Vertex Operators of Admissible Modules of $U_q(C^{…
We construct a representation of $U_q(\widehat{sl}_2)$ at level $-1/2$ by using the bosonic Fock spaces. The irreducible modules are obtained as the kernel of a certain operator, in contrast to the construction by Feingold and Frenkel for…
Vertex operators associated with level two $U_q(\widehat{sl}_2)$ modules are constructed explicitly using bosons and fermions. An integral formula is derived for the trace of products of vertex operators. These results are applied to give…
We show how the states constructed from the action of the modes of bosonized vertex operators, that intertwine $U_q(\widehat{sl(2)})$ modules, are related to $q$-zonal functions.
We calculate the exchange relations of vertex operators of $U_q(\hat{sl_2})$ at level-two from its bosonic realization. The corresponding invertibility relation of type I vertex operators is also studied.
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)…
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…
We construct bosonized vertex operators (VOs) and conjugate vertex operators (CVOs) of $U_q(su(2)_k)$ for arbitrary level $k$ and representation $j\leq k/2$. Both are obtained directly as two solutions of the defining condition of vertex…
We construct explicitly the quantum symplectic affine algebra $U_q(\widehat{sp}_{2n})$ using bosonic fields. The Fock space decomposes into irreducible modules of level -1/2, quantizing the Feingold-Frenkel construction for q=1.
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…
A bosonization scheme of the $q$-vertex operators of $\uqa$ for arbitrary level is obtained. They act as intertwiners among the highest weight modules constructed in a bosonic Fock space. An integral formula is proposed for $N$-point…
We construct explicitly the $q$-vertex operators (intertwining operators) for the level one modules $V(\Lambda_i)$ of the classical quantum affine algebras of twisted types using interacting bosons, where $i=0, 1$ for $A_{2n-1}^{(2)}$,…
Free field relization of vertex operators for lvel two modules of $U_q(\hat{sl(2)})$ is shown through the free field relization of the modules given by Idzumi in Ref.[4,5]. We constructed types I and II vertex operators when the spin of the…
The level 1 highest weight modules of the quantum affine algebra $U_q(\widehat{\frak{sl}}_n)$ can be described as spaces of certain semi-infinite wedges. Using a $q$-antisymmetrization procedure, these semi-infinite wedges can be realized…
$q$-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…
We consider two different methods of associating vertex algebraic structures with the level $1$ principal subspaces for $U_q (\widehat{\mathfrak{sl}}_2)$. In the first approach, we introduce certain commutative operators and study the…
We give a bosonization of the quantum affine superalgebra $U_q(\widehat{sl}(N|1))$ for an arbitrary level $k \in {\bf C}$. The bosonization of level $k \in {\bf C}$ is completely different from those of level $k=1$. From this bosonization,…
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 bosonize certain components of level $\ell$ $U_q(\hat{sl}_2)$-intertwiners of $(\ell + 1)$-dimensions. For $\ell = 2$, these intertwiners, after certain modification by bosonic vertex operators, are added to the algebra $U_q(\hat{sl}_2)$…
We construct level one representations of the quantum affine algebra $U_q(G_2^{(1)})$ by vertex operators from bosonic fields.
We construct a bosonization of the quantum superalgebra $U_q(\hat{sl}(N|1))$ for an arbitrary level $k$. We construct the screening that commutes with the quantum superalgebra for an arbitrary level $k \neq -N+1$. We propose a bosonization…