Mathematics – Algebraic Geometry
Scientific paper
2004-11-16
Mathematics
Algebraic Geometry
16 pages
Scientific paper
We discuss a special eigenstate of the quantized periodic Calogero-Moser system associated to a root system. This state has the property that its eigenfunctions, when regarded as multivalued functions on the space of regular conjugacy classes in the corresponding semisimple complex Lie group, transform under monodromy according to the complex reflection representation of the affine Hecke algebra.We show that this endows the space of conjugacy classes in question with a projective structure. For a certain parameter range this projective structure underlies a complex hyperbolic structure. If in addition a Schwarz type of integrality condition is satisfied, then it even has the structure of a ball quotient minus a Heegner divisor. For example, the case of the root system E_8 with the triflection monodromy representation describes a special eigenstate for the system of 12 unordered points on the projective line under a particular constraint.
Couwenberg Wim
Heckman Gert
Looijenga Eduard
No associations
LandOfFree
On the geometry of the Calogero-Moser system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the geometry of the Calogero-Moser system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the geometry of the Calogero-Moser system will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-212539