Fusion ring revisited

Abstract

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.

To appear in Contemporary Mathematics

References in corpus (2)

• Tensor invariants, Saturation problems, and Dynkin automorphisms
• Conformal blocks, Verlinde formula and diagram automorphisms

Cited by in corpus (8)

• Conformal blocks, Verlinde formula and diagram automorphisms
• Conformal blocks for Galois covers of algebraic curves
• Twisted conformal blocks and their dimension
• Twisted Conjugation on Connected Simple Lie Groups and Twining Characters
• Twisted Affine Lie Algebras, Fusion Algebras, and Congruence Subgroups
• Affine Pieri rule for periodic Macdonald spherical functions and fusion rings
• Twisted Moduli Spaces and Duistermaat-Heckman Measures
• Fusion Rings and Modular Invariance for Affine Lie Algebras: A Double Affine Weyl Group Formulation