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Thinness of some hypergeometric groups in 
$\mathrm{Sp}(6)$
Published online by Cambridge University Press: 02 May 2024
Abstract
We show the thinness of 
$7$ of the 
$40$ hypergeometric groups having a maximally unipotent monodromy in 
$\mathrm{Sp}(6)$.
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust
References
Bajpai, J., Dona, D., Singh, S. and Singh, S. V., Symplectic hypergeometric groups of degree six, J. Algebra 575 (2021), 256–273.CrossRefGoogle Scholar
Bajpai, J., Dona, D. and Nitsche, M., Arithmetic and thin monodromy in Sp(6), arXiv:2112.12111.Google Scholar
Bajpai, J. and Singh, S., On orthogonal hypergeometric groups of degree five, Trans. Am. Math. Soc. 372(11) (2019), 7541–7572.CrossRefGoogle Scholar
Benson, D., Campagnolo, C., Ranicki, A. and Rovi, C., Cohomology of symplectic groups and Meyer’s signature theorem, Algebr. Geom. Topol. 18(7) (2018), 4069–4091.CrossRefGoogle Scholar
Beukers, F. and Heckman, G., Monodromy for the hypergeometric function
$_n{F}_{n-1}$
, Invent. Math. 95(2) (1989), 325–354.CrossRefGoogle Scholar
$_n{F}_{n-1}$
, Invent. Math. 95(2) (1989), 325–354.CrossRefGoogle ScholarBrav, C. and Thomas, H., Thin monodromy in Sp(4), Compos. Math. 150(3) (2014), 333–343.CrossRefGoogle Scholar
Detinko, A. S., Flannery, D. L. and Hulpke, A., Experimenting with symplectic hypergeometric monodromy groups, Exp. Math. 32(1) (2021), 88–96. DOI: 10.1080/10586458.2020.1780516.CrossRefGoogle Scholar
Fuchs, E., The ubiquity of thin groups. Thin groups and superstrong approximation, Math. Sci. Res. Inst. Publ., vol. 61 (Cambridge University Press, Cambridge, 2014), 73–92,Google Scholar
Fuchs, E., Meiri, C. and Sarnak, P., Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions, J. Eur. Math. Soc. (JEMS) 16(8) (2014), 1617–1671.CrossRefGoogle Scholar
Hofmann, J. and van Straten, D., Some monodromy groups of finite index in Sp4 (Z) math, arXiv:1312.3063.Google Scholar
Lyndon, R. C. and Schupp, P. E., Combinatorial group theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 89 (Springer, Berlin, 1977).Google Scholar
Sarnak, P., Notes on thin matrix groups. Thin groups and superstrong approximation, Math. Sci. Res. Inst. Publ., vol. 61 (Cambridge University Press, Cambridge, 2014), 343–362.Google Scholar
Singh, S., Arithmeticity of four hypergeometric monodromy groups associated to Calabi-Yau threefolds, Int. Math. Res. Not. (IMRN) 2015(18) (2015), 8874–8889.CrossRefGoogle Scholar
Singh, S., Orthogonal hypergeometric groups with a maximally unipotent monodromy, Exp. Math. 24(4) (2015), 449–459.CrossRefGoogle Scholar
Singh, S., Arithmeticity of some hypergeometric monodromy groups in Sp(4, J. Algebra 473 (2017), 142–165.CrossRefGoogle Scholar
Singh, S. and Venkataramana, T. N., Arithmeticity of certain symplectic hypergeometric groups, Duke Math. J. 163(3) (2014), 591–617.CrossRefGoogle Scholar
Swan, R. G., Groups of cohomological dimension one, J. Algebra 12(4) (1969), 585–610.CrossRefGoogle Scholar
Venkataramana, T. N., Image of the Burau Representation at
$d$
-th roots of unity, Ann. Math. 179(3) (2014), 1041–1083.CrossRefGoogle Scholar
$d$
-th roots of unity, Ann. Math. 179(3) (2014), 1041–1083.CrossRefGoogle ScholarVenkataramana, T. N., Hypergeometric groups of orthogonal type, J. Eur. Math. Soc. (JEMS) 19(2) (2017), 581–599.CrossRefGoogle Scholar