Commensurability and Arithmetic Equivalence for Orthogonal Hypergeometric Monodromy Groups

References

• [Alekseevskij et al. 93] D. V. Alekseevskij, È. B. Vinberg, and A. S. Solodovnikov, “Geometry of Spaces of Constant Curvature.” In Geometry II, pp. 1–138, Encyclopedia Math. Sci., vol. 29. Berlin: Springer, 1993.
   Google Scholar
• [Bajpai and Singh 17] J. Bajpai and S. Singh, “On Orthogonal Hypergeometric Groups of Degree Five.” Preprint, Preprint, arXiv:1706.08791 [math.GR] (2017).
   Google Scholar
• [Beukers and Heckman 89] F. Beukers and G. Heckman, “Monodromy for the Hypergeometric Function nFn − 1.” Invent. Math. 95: 2 (1989), 325–354.
   Web of Science ®Google Scholar
• [Borel 69] A. Borel, “Introduction Aux Groupes Arithmétiques.” In Publications de l’Institut de Mathématique de l’Université de Strasbourg, XV, Actualités Scientifiques et Industrielles, vol. 1341. Paris: Hermann, 1969.
   Google Scholar
• [Borel and Harish-Chandra 62] A. Borel and Harish-Chandra, “Arithmetic Subgroups of Algebraic Groups.” Ann. Math. 75: 2 (1962), 485–535.
   Google Scholar
• [Brav and Thomas 14] C. Brav and H. Thomas, “Thin Monodromy in Sp(4).” Compos. Math. 150: 3 (2014), 333–343.
   Web of Science ®Google Scholar
• [Cassels 78] J. W. S. Cassels, Rational Quadratic Forms (London Mathematical Society Monographs), vol. 13. London-New York: Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], 1978.
   Google Scholar
• [Fuchs 14] E. Fuchs, “The Ubiquity of Thin Groups.” In Thin Groups and Superstrong Approximation, pp. 73–92, Math. Sci. Res. Inst. Publ., vol. 61. Cambridge: Cambridge University Press, 2014.
   Google Scholar
• [Fuchs et al. 14] E. Fuchs, C. Meiri, and P. Sarnak, “Hyperbolic Monodromy Groups for the Hypergeometric Equation and Cartan Involutions.” J. Eur. Math. Soc. 16: 8 (2014), 1617–1671.
   Web of Science ®Google Scholar
• [Gromov and Piatetski-Shapiro 87] M. Gromov and I. Piatetski-Shapiro, “Non-Arithmetic Groups in Lobachevsky Spaces.” Publications Mathématiques de l’i.h.é.s. 66: 3 (1987), 93–103.
   Google Scholar
• [Hofmann and van Straten 15] J. Hofmann and D. van Straten, “Some Monodromy Groups of Finite Index in Sp4(Z).” J. Aust. Math. Soc. 99: 1 (2015), 48–62.
   Web of Science ®Google Scholar
• [Levelt 61] A. H. M. Levelt, “Hypergeometric Functions.” PhD diss., University of Amsterdam, Drukkerij Holland N. V., Amsterdam, 1961.
   Google Scholar
• [Margulis 91] G. A. Margulis, “Discrete Subgroups of Semisimple Lie Groups.” In Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 17, edited by Series Editors: L. Ambrosio, V. Baladi, G. M. Greuel, M. Gromov, G. Huisken, J. Jost, J. Kollár, G. Laumon, U. Tillmann, J. Tits, D. B. Zagier. Berlin: Springer-Verlag, 1991.
   Google Scholar
• [Meyer 15] Jeffrey S. Meyer, “Totally Geodesic Spectra of Arithmetic Hyperbolic Spaces.” Trans. Amer. Math. Soc. 369: 11 (2017), 7549–7588. https://doi.org/10.1090/tran/6970.
   Web of Science ®Google Scholar
• [O’Meara 63] O. T. O’Meara, “Introduction to Quadratic Forms.” In Die Grundlehren der Mathematischen Wissenschaften, vol. 117, edited by Editors-in-chief: Chenciner, Alain, Coates, John, Varadhan, S.R.S. Series Editors: M. Berger, P. de la Harpe, N. J. Hitchin, A. Kupiainen, G. Lebeau, F. H. Lin, S. Mori, B. C. Ngo, D. Serre, N. J. A. Sloane, A. Vershik, M. Waldschmidt. New York: Academic Press, Inc.; Berlin-Göttingen-Heidelberg: Springer-Verlag, 1963.
   Google Scholar
• [Raghunathan 72] M. S. Raghunathan, “Discrete Subgroups of Lie Groups.” In Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 68, edited by Series Editors: P. R. Halmos, P. Hilton, R. Remmert, B. Szökefalvi-Nagy. New York: Springer, 1972.
   Google Scholar
• [Sage 16] Sage, Sagemath, the Sage Mathematics Software System, Version 7.1, Available at http://www.sagemath.org, March 2016.
   Google Scholar
• [Sarnak 14] P. Sarnak, “Notes on Thin Matrix Groups.” In Thin Groups and Superstrong Approximation, pp. 343–362, Math. Sci. Res. Inst. Publ., vol. 61. Cambridge: Cambridge University Press, 2014.
   Google Scholar
• [Serre 73] J.-P. Serre, “A Course in Arithmetic.” In (Translated from the French) Graduate Texts in Mathematics, vol. 7, edited by Series Editors: S. Axler, F. W. Gehring, P. R. Halmos, p.14. New York: Springer, 1973.
   Google Scholar
• [Singh 15a] S. Singh, “Arithmeticity of Four Hypergeometric Monodromy Groups Associated to Calabi-Yau Threefolds.” Int. Math. Res. Not. 18 (2015a), 8874–8889.
   Google Scholar
• [Singh 15b] S. Singh, “Orthogonal Hypergeometric Groups with a Maximally Unipotent Monodromy.” Exp. Math. 24: 4 (2015b), 449–459.
   Web of Science ®Google Scholar
• [Singh 17] S. Singh, “Arithmeticity of Some Hypergeometric Monodromy Groups in sp(4).” J. Algebra 473 (2017), 142–165. https://doi.org/10.1016/j.jalgebra.2016.09.030.
   Web of Science ®Google Scholar
• [Singh and Venkataramana 14] S. Singh and T. N. Venkataramana, “Arithmeticity of Certain Symplectic Hypergeometric Groups.” Duke Math. J. 163: 3 (2014), 591–617.
   Web of Science ®Google Scholar
• [The GAP Group 16] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.8.4, June 2016.
   Google Scholar
• [Venkataramana 14] T. N. Venkataramana, “Hypergeometric Groups of Orthogonal Type.” J. Eur. Math. Soc. Preprint, 19: 2 (2017), 581–599. https://doi.org/10.4171/JEMS/675.
   Web of Science ®Google Scholar