A Kac–Weyl character identity
Abstract
The Racah–Speiser algorithm and its generalizations lead to an identity involving sums of Kac–Weyl characters, and here we recover this identity through an explicit quantization of Chern–Simons theory. One can use this identity to prove inequalities that constrain the fusion coefficients Nμνl in the case of rational conformal field theories that descend from current algebras. It also leads to a statement regarding the conjugacy symmetry of the sums of squares of fusion coefficients for current algebras admitting complex representations.
Fields of Study & Subjects
Advanced Operator Algebra Research
Algebraic structures and combinatorial models
Advanced Algebra and Geometry
Publication details
- Journal / source
- Journal of Mathematical Physics
- Volume
- 67
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN