96 research outputs found
Fusion rings for degenerate minimal models
We study fusion rings for degenerate minimal models ( case) for N=0 and
N=1 (super)conformal algebras. We consider a distinguished family of modules at
the level and and show that the corresponding fusion rings are
isomorphic to the representation rings for and
respectively.Comment: Revised and enlarged version. It includes all the results from
math.QA/0101165 (to appear in Journal of Algebra
Formal differential operators, vertex operator algebras and zeta--values , II
We introduce certain correlation functions (graded --traces) associated to
vertex operator algebras and superalgebras which we refer to as --point
functions. These naturally arise in the studies of representations of Lie
algebras of differential operators on the circle \cite{Le1}--\cite{Le2},
\cite{M}. We investigate their properties and consider the corresponding graded
--traces in parallel with the passage from genus 0 to genus 1 conformal
field theory. By using the vertex operator algebra theory we analyze in detail
correlation functions in some particular cases. We obtain elliptic
transformation properties for --traces and the corresponding --difference
equations. In particular, our construction leads to correlation functions and
--difference equations investigated by S. Bloch and A. Okounkov \cite{BO}.Comment: 46 pages, LaTeX (10pt, small font), 1 figure, BibTe
On W-algebra extensions of (2,p) minimal models: p > 3
This is a continuation of arXiv:0908.4053, where, among other things, we
classified irreducible representations of the triplet vertex algebra W_{2,3}.
In this part we extend the classification to W_{2,p}, for all odd p>3. We also
determine the structure of the center of the Zhu algebra A(W_{2,p}) which
implies the existence of a family of logarithmic modules having L(0)-nilpotent
ranks 2 and 3. A logarithmic version of Macdonald-Morris constant term identity
plays a key role in the paper.Comment: 19 page
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