Spectral measures associated to rank two Lie groups and finite subgroups of $GL(2,\mathbb{Z})$
| Autor: | Evans, David E., Pugh, Mathew |
|---|---|
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Communications in Mathematical Physics 343 (2016), 811-850 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00220-015-2434-5 |
| Popis: | 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 $\mathbb{T}^2$ and are invariant under an action of the corresponding Weyl group, which is a subgroup of $GL(2,\mathbb{Z})$. Here we consider spectral measures invariant under an action of the other finite subgroups of $GL(2,\mathbb{Z})$. These spectral measures are all associated with fundamental representations of other rank two Lie groups, namely $\mathbb{T}^2=U(1) \times U(1)$, $U(1) \times SU(2)$, $U(2)$, $SU(2) \times SU(2)$, $SO(4)$ and $PSU(3)$. Comment: 39 pages, 46 figures; new results added in Section 9, new Section 3.2, minor improvements to exposition throughout |
| Databáze: | arXiv |
| Externí odkaz: |
|