Arithmetic Monodromy in Sp(2n)
Group Theory
2022-09-16 v1
Abstract
Based on a result of Singh--Venkataramana, Bajpai--Dona--Singh--Singh gave a criterion for a discrete Zariski-dense subgroup of Sp(2n,Z) to be a lattice. We adapt this criterion so that it can be used in some situations that were previously excluded. We apply the adapted method to subgroups of Sp(6,Z) and Sp(4,Z) that arise as the monodromy groups of hypergeometric differential equations. In particular, we show that out of the 40 maximally unipotent Sp(6) hypergeometric groups more than half are arithmetic, answering a question of Katz in the negative.
Keywords
Cite
@article{arxiv.2209.07402,
title = {Arithmetic Monodromy in Sp(2n)},
author = {Jitendra Bajpai and Daniele Dona and Martin Nitsche},
journal= {arXiv preprint arXiv:2209.07402},
year = {2022}
}
Comments
6 pages. Contains some results that were previously part of arXiv:2112.12111v2