New integrable hierarchies from vertex operator representations of polynomial Lie algebras

Principal Vertex Operator Representations For Toroidal Lie Algebras

Vertex operators discovered by physicists in string theory have turned out to be important objects in mathematics. One can use vertex operators to construct various realizations of the irreducible highest weight representations for affine Kac-Moody algebras. Two of these, the principal and homogeneous realizations, are of particular interest. The principal vertex operator construction for the a...

Representations of vertex operator algebras

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras An(V ) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is a semisimple associative algebra. 2000MSC:17B69

Representations of Ternary Code Vertex Operator Algebras

Twisted Representations of Vertex Operator Algebras

Let V be a vertex operator algebra and g an automorphism of finite order. We construct an associative algebra Ag(V ) and a pair of functors between the category of Ag(V )-modules and a certain category of admissible g-twisted V -modules. In particular, these functors exhibit a bijection between the simple modules in each category. We give various applications, including the fact that the comple...

Vertex operator algebras associated to type G affine Lie algebras

Article history: Received 15 November 2010 Available online 11 May 2011 Communicated by Masaki Kashiwara