On the Mathieu conjecture for Sp(N) and G2

As a direct continuation of Zwart [J. Math. Phys. 64(10), 101701 (2023)], which is built on the work of Müger and Tuset [Indagationes Math. 35(1), 114 (2024)], we reduce the Mathieu conjecture, formulated by Mathieu [Algèbra 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 Sp(N) and G2 to a conjecture involving functions over Rn×(S1)m with n,m∈N0. The proofs rely on Euler-style parametrizations of these groups, a specific version of the KAK decomposition, which we discuss and prove.