ABSTRACT
Invariants are computed of quadratic forms associated with orthogonal hypergeometric groups of degree five. Some commensurabilities are then determined between these groups, and it is established that some thin groups cannot be conjugated to each other.
2010 AMS SUBJECT CLASSIFICATION:
Acknowledgments
The authors are grateful to the Max Planck Institute for Mathematics in Bonn, where much of the requisite discussion took place, for its support and hospitality. JB would like to thank Gerhard Hiss and Klaus Lux for many interesting conversations during his visit to Aachen, and thanks the Mathematical Institute of the University of Bern for its hospitality. The authors are grateful to the referee at Experimental Mathematics for their comments. The authors are grateful to the referee at Experimental Mathematics for their comments.