相关论文: Wakimoto realizations of current algebras: an expl…
It is known from a work of Feigin and Frenkel that a Wakimoto type, generalized free field realization of the current algebra $\widehat{\cal G}_k$ can be associated with each parabolic subalgebra ${\cal P}=({\cal G}_0+{\cal G}_+)$ of the…
Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has…
It is well known that the bosonized version of the Wakimoto construction allows the explicit realization of any affine algebra $\widehat{g}$, with arbitrary level $k$ in the homogeneous gradation, in terms of $dim(g)$ free bosonic fields.…
Relaxing first-class constraint conditions in the usual Drinfeld-Sokolov Hamiltonian reduction leads, after symmetry fixing, to realizations of W algebras expressed in terms of all the J-current components. General results are given for G a…
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…
We construct a realization of the quantum affine algebra $U_q(\widehat{sl_N})$ of an arbitrary level $k$ in terms of free boson fields. In the $q\!\rightarrow\! 1$ limit this realization becomes the Wakimoto realization of $\widehat{sl_N}$.…
We construct a free field realization of the elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ for arbitrary level $k \neq 0,-N$. We study Drinfeld current and the screening current associated with $U_{q,p}(\hat{sl_N})$ for arbitrary level…
The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G=so(4,2), unitary representations of the conformal and Poincare algebras are…
A boson representation of the quantum affine algebra $U_q(\widehat{\sl}_2)$ is realized based on the Wakimoto construction. We discuss relations with the other boson representations.
We generalize some results concerning affine algebras at the critical level to the corresponding quantum algebras. In particular, we show that the Wakimoto realization provides a homomorphism of Poisson algebras from the center of a quantum…
In a vertex algebraic framework, we present an explicit description of the twisted Wakimoto realizations of the affine Lie algebras in correspondence with an arbitrary finite order automorphism and a compatible integral gradation of a…
By generalizing the Miura transformation for $\Ww_N$ to other classical $\Ww$ algebras obtained by hamiltonian reduction, we find realisations of these algebras in terms of relatively simple non-abelian current algebras, e.g.…
In this paper we consider Wakimoto free field realizations of simple affine Lie algebras, a subject already much studied. We present three new sets of results. (i) Based on quantizing differential operator realizations of the corresponding…
We present the extension of the Wakimoto construction to the $su(2)_k$ quantum current algebra and its associated $Z_k$ quantum parafermion algebra. This construction is achieved in terms of various deformations of three classical free…
We give bosonizations of the superalgebras $U_q(\hat{sl}(N|1))$ and $U_{q,p}(\hat{sl}(N|1))$ for an arbitrary level $k \in {\bf C}$. We introduce the submodule by the $\xi$-$\eta$ system, that we call the $q$-Wakimoto realization.
It is well-known that the chiral WZNW Bloch waves satisfy a quadratic classical exchange algebra which implies the affine Kac-Moody algebra for the corresponding currents. We here obtain a direct derivation of the exchange algebra by…
We construct new families of positive energy representations of affine vertex algebras together with their free field realizations by using localization technique. We introduce the twisting functor T_\alpha on the category of modules over…
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,…
The quantum toroidal algebra of $gl_1$ provides many deformed W-algebras associated with (super) Lie algebras of type A. The recent work by Gaiotto and Rapcak suggests that a wider class of deformed W-algebras including non-principal cases…
(Affine) $\mathcal{W}$-algebras are a family of vertex algebras defined by the generalized Drinfeld-Sokolov reductions associated with a finite-dimensional reductive Lie algebra $\mathfrak{g}$ over $\mathbb{C}$, a nilpotent element $f$ in…