Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 5

Special issue on “Subfactors and Related Topics” in memory of Vaughan Jones

Guest Editors: Dietmar Bisch, Arthur Jaffe, Yasuyuki Kawahigashi, and Zhengwei Liu

Spectral measures for $Sp(2)$

Pages: 2249 – 2305

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n5.a1

Authors

David Evans (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)

Mathew Pugh (School of Mathematics, Cardiff University, Cardiff, Wales, United Kingdom)

Abstract

Spectral measures provide invariants for braided subfactors via fusion modules. In this paper we study joint spectral measures associated to the compact connected rank two Lie group $SO(5)$ and its double cover the compact connected, simply-connected rank two Lie group $Sp(2)$, including the McKay graphs for the irreducible representations of $Sp(2)$ and $SO(5)$ and their maximal tori, and fusion modules associated to the $Sp(2)$ modular invariants.

Keywords

spectral measures, $Sp(2)$, subfactor, fusion ring, fusion module

2010 Mathematics Subject Classification

05C50, 43A45, 46L37

Received 18 September 2022

Accepted 10 November 2022

Published 30 January 2024