2014/04/30 by David E. Evans, Mathew Pugh
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Algebra and Geometry #Analytic Number Theory Research #Invariant (physics) #Lie group #Mathematical Analysis and Transform Methods #Maximal torus #Rank (graph theory) #Simple Lie group #Spectral properties #Torus #hep-th #math-ph #math.MP #math.OA
paper · pdf · doi:10.1007/s00220-015-2434-5
published as Communications in Mathematical Physics 343 (2016), 811-850 · 39 pages, 46 figures; new results added in Section 9, new Section 3.2, minor improvements to exposition throughout
arxiv created 2015/02/23 · openalex publication_date 2016/03/22 · arxiv updated 2016/04/25 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
Spectral measures for fundamental representations of the rank two Lie groups SU(3), Sp(2) and G2 have been studied. Since these groups have rank two, these spectral measures can be defined as measures over their maximal torus \mathbbT2 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 \mathbbT2=U(1) × U(1), U(1) × SU(2), U(2), SU(2) × SU(2), SO(4) and PSU(3).