相关论文: Free field representations for the affine superalg…

This paper studies a subset of the free semi-group $F_k$ with letters in a field $k$ which has some interesting arithmetic and combinatorial properties.

We consider the spin $k/2$ XXZ model in the antiferomagnetic regime using the free field realization of the quantum affine algebra $\uqa$ of level $k$. We give a free field realization of the type II $q$-vertex operator, which describes…

This article presents a new relation between the basic representation of split real simply-laced affine Kac-Moody algebras and finite dimensional representations of its maximal compact subalgebra $\mathfrak{k}$. We provide infinitely many…

Using a unified and systematic scheme, the free field realization of irreducible representations of osp(2|2) is constructed. By using these realization, the correlation functions of N=2 super-conformal model based on osp(2|2) symmetry and…

The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…

We relate two apparently different bases in the representations of affine Lie algebras of type A: one arising from statistical mechanics, the other from gauge theory. We show that the two are governed by the same combinatorics and therefore…

Since 1999 it became obvious that the would be `isomorphism' between the affine $\hat sl(2)$ algebra and the N=2 superconformal algebras, proposed by some authors, simply does not work. However, this issue was never properly discussed in…

We present a manifestly $N=2$ supersymmetric formulation of $N=2$ super-$W_3$ algebra (its classical version) in terms of the spin 1 and spin 2 supercurrents. Two closely related types of the Feigin-Fuchs representation for these…

We classify, up to isomorphism, the group gradings on the non-exceptional classical simple Lie superalgebras, except for type A(1,1), over an algebraically closed field of characteristic zero. To this end, we study graded-simple and…

In our earlier papers we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV)…

We prove that critical and subcritical N=2 string theory gives a realization of an N=2 superfield extension of the topological conformal algebra. The essential observation is the vanishing of the background charge.

We use Nakajima's geometric approach to representations of quantum affine algebras and recent results on explicit descriptions of specific canonical basis elements, to derive closed positive formulas for certain decomposition numbers of…

We formulate the general construction for singular vectors in Verma modules of the affine sl(2|1) superalgebra. We then construct sl(2|1) representations out of the fields of the non-critical N=2 string. This allows us to extend naturally…

We present two novel proofs of the known classification of connected affine algebraic supergroups $G$ such that $\operatorname{Rep}G$ is semisimple. The proofs are geometrically motivated, although both rely on an algebraic lemma that…

We introduce a new approach to the study of finite-dimensional representations of the quantum group of the affine Lie superalgebra $\mathrm{L}\mathfrak{gl}_{M|N}=\mathbb{C}[t,t^{-1}]\otimes\mathfrak{gl}_{M|N}$ ($M\neq N$). We explain how…

The quantum affine $\CU_q (\hat{sl(2)}) $ symmetry is studied when $q^2$ is an even root of unity. The structure of this algebra allows a natural generalization of N=2 supersymmetry algebra. In particular it is found that the momentum…

In this article we present some probably unexpected (in our opinion) properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra ym(n) on n…

A review is presented of the recently obtained expressions for conformal blocks for {\it admissible} representations in $SL(2)$ current algebra based on the Wakimoto free field construction. In this realization one needs to introduce a…

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…

In this work, free multivariate skew polynomial rings are considered, together with their quotients over ideals of skew polynomials that vanish at every point (which includes minimal multivariate skew polynomial rings). We provide a full…