What question did this study set out to answer?

The aim is to recover a Kac–Weyl character identity using a quantization of Chern–Simons theory.

A Kac–Weyl character identity

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This work demonstrates the Kac–Weyl character identity in rational conformal field theories, indicating implications for fusion coefficients.

The aim is to recover a Kac–Weyl character identity using a quantization of Chern–Simons theory.
Utilized the Racah–Speiser algorithm and its generalizations
Performed explicit quantization of Chern–Simons theory
Analyzed the implications for fusion coefficients in conformal field theories
Confirmed the Kac–Weyl character identity
Proved inequalities constraining fusion coefficients Nμνl
Established conjugacy symmetry for fusion coefficient squares in current algebras with complex representations

Baker et al. (2026) studied this question.

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This work demonstrates the Kac–Weyl character identity in rational conformal field theories, indicating implications for fusion coefficients.