On the Mathieu conjecture for SU(N) and SO(N)

Abstract

Building on work of Müger and Tuset [arXiv.2210.06582 (2022)], we reduce the Mathieu conjecture, formulated by Mathieu in 1997 [Algebre Non Commutative, Groupes Quantiques et Invariants, edited by Alex, J. and Cauchon, G. (Société Mathématique de France, Reims, 1997), Vol. 2, pp. 263–279], for SU(N) to a simpler conjecture in purely abelian terms. We sketch a similar reduction for SO(N). The proofs rely on Euler-style parametrizations of these groups, which we discuss including proofs.