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Representation Theory of Code Vertex Operator Algebra

โœ Scribed by Masahiko Miyamoto

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
359 KB
Volume
201
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

We study the representation theory of code vertex operator algebras M D ลฝ . VOAs constructed from an even binary linear code D. Our main purpose is to study, using the representation theory of M , the structure of VOA V containing a D 1 set of mutually orthogonal rational conformal vectors with central charge such 2 that the sum of them is the Virasoro element of V. The most famous example of such VOAs is the Moonshine VOA V h . If a simple VOA V contains such a set of conformal vectors, then V has an elementary Abelian automorphism 2-group P generated by involutions. As a P-module, V has a decomposition V s [ V g I r rลฝ P .

as the direct sum of weight spaces V of P. It was proved that V is an irreducible V P -module. Therefore, we can expect that the classification of irreducible V P -modules and their fusion rules will determine the structure of V. We will show that the fixed point space V P is isomorphic to a code VOA M of some binary linear even D code D, and then study and classify all irreducible M -modules and compute the D fusion rules of some of them.

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We study a vertex operator algebra whose Virasoro element is a sum of pairwise 1 orthogonal rational conformal vectors with central charge . The most important 2 example is the moonshine module V h . In particular, we construct a series of vertex operator algebras whose full automorphism groups are