Spectral Measures Associated to Rank two Lie Groups and Finite Subgroups of {GL(2,{Z})}

Spectral measures for fundamental representations of the rank two Lie groups SU(3), Sp(2) and G ₂ have been studied. Since these groups have rank two, these spectral measures can be defined as measures over their maximal torus {{T}^2} and are invariant under an action of the corresponding Weyl group, which is a subgroup of {GL(2,{Z})}. Here we consider spectral measures invariant under an action of the other finite subgroups of {GL(2,{Z})}. These spectral measures are all associated with fundamental representations of other rank two Lie groups, namely {{T}^2=U(1) × U(1)}, {U(1) × SU(2)}, U(2), {SU(2) × SU(2)}, SO(4) and PSU(3).