Monodromy of hypergeometric functions and non-lattice integral monodromy

 Access to full text

 Full (PDF)

1. [1] APPEL, P., a) CR Acad. Sci., Paris, 16 février 1880 ; b) Sur les fonctions hygergéométriques de deux variables, J. de Math., 3e ser., VIII (1882), 173-216. 
2. [2] BOREL, A., a) Density properties for certain subgroups of semi-simple groups without compact components, Ann. of Math., 72 (1960), 179-188 ; b) Reduction theory for arithmetic groups, Proc. Symposia in Pure Math., IX (1966), 20-25. Zbl0094.24901MR23 #A964
3. [3] BOREL, A.-Harish Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math., 75 (1962), 485-535. Zbl0107.14804MR26 #5081
4. [4] BOURBAKI, N., Groupes et Algèbres de Lie, chap. V, Paris, Herman, 1968. Zbl0186.33001
5. [5] EULER, L., “Specimen transformations singularis serierum”, Sept. 3, 1778, Nova Acta Petropolitana, XII (1801), 58-78. 
6. [6] FRICKE, R., and KLEIN, F., Vorlesungen über die Theorie der Automorphen Functionen, Bd. I, Leipzig, Teubner, 1897. JFM28.0334.01
7. [7] FOX, R. H., Covering spaces with singularities, in Lefschetz Symposium, Princeton Univ. Press (1957), 243-262. Zbl0079.16505MR23 #A626
8. [8] FUCHS, L., Zur Theorie der linearen Differential gleichungen mit verändlerichen Coeffizienten, J. r. und angew. Math., 66 (1866), 121-160. 
9. [9] HERMITE, C., Sur quelques équations différentielles linéaires, J. r. und angew. Math., 79 (1875), 111-158. 
10. [10] HOCHSCHILD, G. P., The Structure of Lie Groups, Holden-Day, San Francisco, 1965. Zbl0131.02702MR34 #7696
11. [11] KNESER, M., Strong approximation, Proc. of Symposia in Pure Math., IX (1966), 187-196. Zbl0201.37904MR35 #4225
12. [12] LAURICELLA, Sulle funzioni ipergeometriche a piu variabili, Rend. di Palermo, VII (1893), 111-158. JFM25.0756.01
13. [13] LE VAVASSEUR, R., Sur le système d'équations aux dérivées partielles simultanées auxquelles satisfait la série hypergéométrique à deux variables, J. Fac. Sci. Toulouse, VII (1896), 1-205. JFM25.0608.02
14. [14] MOSTOW, G. D., a) Existence of nonarithmetic monodromy groups, Proc. Nat. Acad. Sci., 78 (1981), 5948-5950 ; b) Generalized Picard lattices arising from half-integral conditions, Publ. Math. I.H.E.S., this volume, 91-106. Zbl0551.32024MR86b:22020
15. [15] MUMFORD, D., Geometric Invariant Theory, Berlin, Springer, 1965. Zbl0147.39304MR35 #5451
16. [16] PICARD, E., a) Sur une extension aux fonctions de deux variables du problème de Riemann relatif aux fonctions hypergéométriques, Ann. ENS, 10 (1881), 305-322 ; b) Sur les fonctions hyperfuchsiennes provenant des séries hypergéométriques de deux variables, Ann. ENS, III, 2 (1885), 357-384 ; c) Id., Bull. Soc. Math. Fr., 15 (1887), 148-152. JFM19.0429.01
17. [17] POCHHAMMER, L., Ueber hypergeometrische Functionen höherer Ordnung, J. r. und angew. Math., 71 (1870), 316-362. JFM02.0265.01
18. [18] RIEMANN, B., Beiträge zur Theorie der durch die Gauss'sche Reihe F(α, β, γ, χ) darstellbaren Functionen, Abh. Kon. Ges. d. Wiss zu Göttingen, VII (1857), Math. Classe, A-22. 
19. [19] SCHAFLI, Ueber die Gauss'sche hypergeometrische Reihe, Math. Ann., III (1871), 286-295. JFM02.0122.02
20. [20] SCHWARZ, H. A., Ueber diejenigen Fälle in welchen die Gauss'sche hypergeometrische Reihe eine algebraisches Function ihres vierten Elementes darstellt, J. r. und angew. Math., 75 (1873), 292-335. JFM05.0146.03
21. [21] TAKEUCHI, K., Commensurability classes of arithmetic discrete triangle groups, J. Fac. Sci. Univ. Tokyo, 24 (1977), 201-212. Zbl0365.20055MR57 #3077
22. [22] TERADA, T., Problème de Riemann et fonctions automorphes provenant des fonctions hypergéometriques de plusieurs variables, J. Math. Kyoto Univ., 13 (1973), 557-578. Zbl0279.32022MR58 #1299
23. [23] TITS, J., Classification of algebraic semi-simple groups, Proc. of Symposia in Pure Math., IX (1966), 33-62. Zbl0238.20052MR37 #309
24. [24] WHITTAKER, E. T., and WATSON, G. N., A course in modern analysis, Cambridge, University Press, 1962. 
25. [25] ZUCKER, S., Hodge theory with degenerating coefficients, I, Ann. of Math., 109 (1979), 415-476. Zbl0446.14002MR81a:14002

1. G. D. Mostow, Generalized Picard lattices arising from half-integral conditions
2. Michael Kapovich, John J. Millson, The relative deformation theory of representations and flat connections and deformations of linkages in constant curvature spaces
3. Jean-Claude Hausmann, Allen Knutson, The cohomology ring of polygon spaces
4. Selim Ghazouani, [unknown]
5. Keiji Matsumoto, On modular functions in 2 variables attached to a family of hyperelliptic curves of genus 3
6. Slavyana Geninska, On arithmetic Fuchsian groups and their characterizations
7. Keiji Matsumoto, Masaaki Yoshida, Configuration space of 8 points on the projective line and a 5-dimensional Picard modular group
8. Michael Gromov, Richard Schoen, Harmonic maps into singular spaces and $p$-adic superrigidity for lattices in groups of rank one
9. Daniel Allcock, James A. Carlson, Domingo Toledo, Hyperbolic geometry and moduli of real cubic surfaces
10. Julien Paupert, Applications moment, polygones de configurations et groupes discrets de réflexions complexes dans $PU(2,1)$