Commensurability and Arithmetic Equivalence for Orthogonal Hypergeometric Monodromy Groups

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.

KEYWORDS:

• hypergeometric group
• monodromy representation
• Quadratic form

2010 AMS SUBJECT CLASSIFICATION:

• Primary: 11E04
• 22E40
• Secondary: 32S40
• 33C80

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.

Additional information

Funding

SS is supported by the inspire Fellowship from the Department of Science and Technology, India. ST is supported by the SNF (Switzerland) grant number PP00P2_157583.