Lower-bounded and grading-restricted twisted modules for affine vertex (operator) algebras

Twisted modules for vertex operator algebras

In this contribution, I explain the general principles of twisted modules for vertex operator algebras in its powerful formulation using formal series, and derive new general relations satisfied by twisted and non-twisted vertex operators. I prove new “equivalence” and “construction” theorems, identifying a very restricted set of sufficient conditions in order to have a twisted module for a ver...

Twisted modules for vertex operator algebras and Bernoulli polynomials

Using general principles of the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an arbitrary twisting automorphism. The construction involves the Bernoulli polynomials in a fundamental way. This is explained through results in the general theory of...

Some Twisted Modules for Framed Vertex Operator Algebras

Vertex Operators for Twisted Quantum Affine Algebras

We construct explicitly the q-vertex operators (intertwining operators) for the level one modules V (Λi) of the classical quantum affine algebras of twisted types using interacting bosons, where i = 0, 1 for A (2) 2n−1, i = 0 for D (3) 4 , i = 0, n for D (2) n+1, and i = n for A (2) 2n . A perfect crystal graph for D (3) 4 is constructed as a by-product.

Twisted vertex representations of quantum affine algebras

Recent interests in quantum groups are stimulated by their marvelous relations with quantum Yang-Baxter equations, conformal field theory, invariants of links and knots, and q-hypergeometric series. Besides understanding the reason of the appearance of quantum groups in both mathematics and theoretical physics there is a natural problem of finding q-deformations or quantum analogues of known st...