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"Subfactors from regular graphs induced by association schemes", Radhakrishnan Balu, 2022

Reviewed January 9, 2024

Citation: Balu, Radhakrishnan. "Subfactors from regular graphs induced by association schemes." arXiv preprint arXiv:2201.07310 (2022).

Web: https://arxiv.org/abs/2201.07310

Tags: Subfactors, 0-categorical, Quantum-groups

This paper proposes a new model of topological quantum computation schemes based on association schemes. It is well-known in the literature that association schemes and character algebras have a deep link with fusion rings:

> Bannai, Eiichi. "Association schemes and fusion algebras (an introduction)." Journal of algebraic Combinatorics 2 (1993): 327-344.

This paper tries to push this further. In the words of the author: "We discussed a... perspective for topological quantum systems and used the connection between fusion algebras central to conformal field theory and association schemes to describe anyon systems". One amazing nugget in this is that the Hamming association scheme, which is the most important association scheme for coding theory, is shown to be intimately linked to the quantum groups U_q(sl_2(C)). This is very nice, because U_q(sl_2(C)) is the most important object in the study of subfactors and topological quantum computing.

Whether or not there is a general framework connecting association schemes to anyonic models is still open.