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Coset construction for winding subalgebras and applications

Peter Bouwknegt
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Abstract

In this paper we review the coset construction for winding subalgebras of affine Lie algebras. We classify all cosets of central charge $\hat c<1$ and calculate their branching rules. The corresponding character identities give certain `doubling formulae' for the affine characters. We discuss some applications of our construction, in particular we find a simple proof of a crucial identity needed for the computation of the level-2 root multiplicities of the hyperbolic Kac-Moody algebra $E_{10}$.

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Peter Bouwknegt. 1997-03-12. Coset construction for winding subalgebras and applications. https://arxiv.org/abs/q-alg/9610013

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