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arXiv · 2210.00792

Complete Positivity of Comultiplication and Primary Criteria for Unitary Categorification

Linzhe Huang·Zhengwei Liu·Sebastien Palcoux·Jinsong Wu
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Abstract

In this paper, we investigate quantum Fourier analysis on subfactors and unitary fusion categories. We prove the complete positivity of the comultiplication for subfactors and derive a primary $n$-criterion of unitary categorifcation of multifusion rings. It is stronger than the Schur product criterion when $n\geq3$. The primary criterion could be transformed into various criteria which are easier to check in practice even for noncommutative, high-rank, high-multiplicity, multifusion rings. More importantly, the primary criterion could be localized on a sparse set, so that it works for multifusion rings with sparse known data. We give numerous examples to illustrate the efficiency and the power of these criteria.

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Linzhe Huang, Zhengwei Liu, Sebastien Palcoux, Jinsong Wu. 2022-10-03. Complete Positivity of Comultiplication and Primary Criteria for Unitary Categorification. https://arxiv.org/abs/2210.00792

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