Related papers: Vertex representations of toroidal special linear …
In this paper, vertex representations of the 2-toroidal Lie superalgebras of type $D(m, n)$ are constructed using both bosonic fields and vertex operators based on their loop algebraic presentation.
A loop-algebraic presentation is given for toroidal Lie superalgebras of classical types. Based on the loop superalgebra presentation free field realizations of toroidal Lie superalgebras are constructed for types $A(m,n)$, $B(m,n)$, C(n)…
We consider general linear superalgebra (type A) and tensor with Laurent polynomial ring in several variables. We then consider the universal central extension of this Lie superalgebra which we call toroidal superalgebra. We give a faithful…
A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains $osp(1|2n)^{(1)}$ as a distinguished subalgebra and behaves similarly to the toroidal Lie superalgebra of type $B(0, n)$.…
In this paper we present the principal construction of the vertex operator representation for toroidal Lie algebras.
Orthosymplectic Lie superalgebras are fundamental symmetries in modern physics, such as massive supergravity. However, their representations are far from being thoroughly understood. In the present paper, we completely determine the…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
Given any representation of an arbitrary Lie algebra L over a field k of characteristic 0, we construct representations of L on bosonic and fermionic Fock space. The method gives an explicit formula for a (sometimes trivial) 2-cocycle in…
Using free fields, we construct a bosonic realization of toroidal Lie algebras of type $A_{2n-1}, A_{2n}, D_{n+1}, D_4$ which are twisted by a Dynkin diagram automorphism. This realization is based upon the recently found…
Generalizing Feingold-Frenkel's construction we use Weyl bosonic fields to construct toroidal Lie algebras of types $A_n, B_n$, $C_n$ and $D_n$ of level $-1, -2, -1/2$ and -2 respectively. In particular, our construction also gives new…
Vertex algebras provide an axiomatic algebraic description of the operator product expansion (OPE) of chiral fields in 2-dimensional conformal field theory. Vertex Lie algebras (= Lie conformal algebras) encode the singular part of the OPE,…
We use a fermionic extension of the bosonic module to obtain a class of B(0,N)-graded Lie superalgebras with nontrivial central extensions.
Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion of a twisted toroidal Lie algebra. In this paper, we construct representations of twisted toroidal Lie algebras from twisted modules…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
This is an expository article on representation theory of toroidal Lie algebras. We summerize all the results on representation theory of toroidal Lie algebras obtained in the last fifteen years. Apart from that a natural genaralization of…
We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex…
To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices, this paper…
We study irreducible representations for the Lie algebra of vector fields on a 2-dimensional torus constructed using the generalized Verma modules. We show that for a certain choice of parameters these representations remain irreducible…
We show that the representation theory for the toroidal extended affine Lie algebras is controlled by a vertex operator algebra which is a tensor product of four VOAs: a sub-VOA of the hyperbolic lattice VOA, two affine VOAs and a Virasoro…
In this paper we introduce a new quantum algebra which specializes to the $2$-toroidal Lie algebra of type $A_1$. We prove that this quantum toroidal algebra has a natural triangular decomposition, a (topological) Hopf algebra structure and…