On the realization of a class of representations
Zhiqiang Yu
Yangzhou University, Yangzhou, P. R. China
![On the realization of a class of $\text{SL}(2,\mathbb{Z})$ representations cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-jncg.png&w=3840&q=90)
Abstract
Let be odd primes and and be irreducible representations of and of dimensions and , respectively. We show that if can be realized as a modular representation associated with a modular fusion category , then . Moreover, if contains a non-trivial étale algebra, then as a braided fusion category, where is a near-group fusion category of type , which gives a partial answer to the conjecture of D. Evans and T. Gannon. We also show that there exists a non-trivial -extension of that contains simple objects of Frobenius–Perron dimension .
Cite this article
Zhiqiang Yu, On the realization of a class of representations. J. Noncommut. Geom. (2024), published online first
DOI 10.4171/JNCG/578