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Self-dual Vertex Operator Superalgebras with Shadows of large minimal weight

Gerald Hoehn
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Abstract

The shadow V' of a self-dual vertex operator superalgebra V is defined as the direct sum of the irreducible modules of its even vertex operator subalgebra $V_{(0)}$ not contained in $V=V_{(0)}+V_{(1)}$. We describe the self-dual ``very nice'' unitary rational vertex operator superalgebras V of rank c whose shadows have the largest possible minimal weights c/8 or c/8-1. The results are analogous to and imply the corresponding results for self-dual binary codes and lattices.

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Gerald Hoehn. 1998-10-01. Self-dual Vertex Operator Superalgebras with Shadows of large minimal weight. https://arxiv.org/abs/q-alg/9608023

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