arXiv Analytics

Sign in

arXiv:1708.07919 [math.RT]AbstractReferencesReviewsResources

Fusion ring revisited

Jiuzu Hong

Published 2017-08-26Version 1

In this note we describe a general elementary procedure to attach a fusion ring to any Kac-Moody algebra of affine type. In the case of untwisted affine algebras, they are usual fusion rings in the literature. In the case of twisted affine algebras, they are exactly the twisted fusion rings defined by the author in [Ho2] via tracing out diagram automorphisms on conformal blocks for appropriate simply-laced Lie algebras. We also relate the fusion ring to the modular S-matrix for any Kac-Moody algebra of affine type.

Comments: comments welcome
Categories: math.RT, math-ph, math.MP, math.QA
Subjects: 17B67, 81T40, 20G44
Related articles: Most relevant | Search more
arXiv:math/0610376 [math.RT] (Published 2006-10-11)
Elementary divisors of the Shapovalov form on the basic representation of Kac-Moody algebras
arXiv:1804.02308 [math.RT] (Published 2018-04-05, updated 2020-07-28)
Commutator relations and structure constants for rank 2 Kac--Moody algebras
arXiv:math/0609349 [math.RT] (Published 2006-09-13, updated 2006-10-02)
On the multiplicities of the irreducible highest weight modules over Kac-Moody algebras

Links

Toolbox