Ising vectors and automorphism groups of commutant subalgebras related to root systems

Details Ising vectors and automorphism groups of commutant subalgebras related to root systems Ising vectors and automorphism groups of commutant subalgebras related to root systems

2005-07-18

arxiv.org/abs/math/0507371v1

Mathematics

Quantum Algebra

33 pages

Scientific paper

In this article we study and obtain a classification of Ising vectors in vertex operator algebras associated to binary codes and $\sqrt{2}$ times root lattices, where an Ising vector is a conformal vector with central charge 1/2 generating a simple Virasoro sub VOA. Then we apply our results to study certain commutant subalgebras related to root systems. We completely classify all Ising vectors in such commutant subalgebras and determine their full automorphism groups.

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