2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149570In 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 $E_{10}$.8 pages. Crucial reference overlooked. Ref added and appropriate changes made, including new title. Old title: `A new coset construction and applications'. Plain TeX with amssym.defQuantum AlgebraHigh Energy Physics - Theory17B67, 17B68, 81R10text