Arithmetic monodromy in $\mathrm{Sp}(2n)$ Article Swipe
Jitendra. Bajpai
,
Daniele Donà
,
Martin Nitsche
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.4171/ggd/940
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.4171/ggd/940
Based on a result of Singh–Venkataramana, Bajpai–Dona–Singh–Singh gave a criterion for a discrete Zariski-dense subgroup of \mathrm{Sp}(2n,\mathbb{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 \mathrm{Sp}(6,\mathbb{Z}) and \mathrm{Sp}(4,\mathbb{Z}) that arise as the monodromy groups of hypergeometric differential equations. In particular, we show that out of the 40 maximally unipotent \mathrm{Sp}(6) hypergeometric groups, more than half are arithmetic, answering a question of Katz in the negative.
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- https://doi.org/10.4171/ggd/940
- OA Status
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https://doi.org/10.4171/ggd/940Digital Object Identifier
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Arithmetic monodromy in $\mathrm{Sp}(2n)$Work title
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articleOpenAlex work type
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2025Year of publication
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2025-11-13Full publication date if available
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Jitendra. Bajpai, Daniele Donà, Martin NitscheList of authors in order
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- Concepts
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Mathematics, Monodromy, Unipotent, Hypergeometric distribution, Pure mathematics, Algebra over a field, Differential (mechanical device), Group (periodic table), Hypergeometric function, Discrete mathematics, Arithmetic, Basic hypergeometric series, Hypergeometric identityTop concepts (fields/topics) attached by OpenAlex
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