Coset construction for winding subalgebras and applications

arXivq-alg/9610013MaRDI QIDQ6502288

P. Bouwknegt

Abstract: In this paper we review the coset construction for winding subalgebras of affine Lie algebras. We classify all cosets of central charge $hatc<1$ 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 $E_{10}$.

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Virasoro and related algebras (17B68) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

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