75 research outputs found
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 vertex operator algebras, including a new identity, which we
call ``modified weak associativity.'' This paper is an announcement. The
detailed proofs will appear elsewhere.Comment: 15 pages, LaTeX, Revised version (to appear in I.M.R.N.
The Rogers--Ramanujan recursion and intertwining operators
We use vertex operator algebras and intertwining operators to study certain
substructures of standard --modules, allowing us to conceptually
obtain the classical Rogers--Ramanujan recursion. As a consequence we recover
Feigin-Stoyanovsky's character formulas for the principal subspaces of the
level 1 standard --modules.Comment: minor change
A logarithmic generalization of tensor product theory for modules for a vertex operator algebra
We describe a logarithmic tensor product theory for certain module categories
for a ``conformal vertex algebra.'' In this theory, which is a natural,
although intricate, generalization of earlier work of Huang and Lepowsky, we do
not require the module categories to be semisimple, and we accommodate modules
with generalized weight spaces. The corresponding intertwining operators
contain logarithms of the variables.Comment: 39 pages. Misprints corrected. Final versio
- …