论文信息 - Cones and ping-pong in three dimensions

Cones and ping-pong in three dimensions

We study the hypergeometric group in GL3(C) with parameters α = ( 14 , 1 2 , 3 4 ) and β = (0, 0, 0). We give a new proof that this group is isomorphic to the free product Z/4Z ∗ Z/2Z by exhibiting a ping-pong table. Our table is determined by a simplicial cone in R3, and we prove that this is the unique simplicial cone (up to sign) for which our construction produces a valid ping-pong table.

Gabriel Frieden | F'elix G'elinas | 'Etienne Soucy

[1] H. Schwarz,et al. Ueber diejenigen Fälle, in welchen die Gaussische hypergeometrische Reihe eine algebraische Function ihres vierten Elementes darstellt. , 1873 .

[2] 野村栄一,et al. 2 , 1900, The Hatak Witches.

[3] H. Thomas,et al. Thin monodromy in Sp(4) , 2012, Compositio Mathematica.

[4] T. Venkataramana. Image of the Burau Representation at $d$-th Roots of unity , 2012, 1205.6543.

[5] Simion Filip,et al. A cyclotomic family of thin hypergeometric monodromy groups in Sp4(R) , 2021 .

[6] Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions , 2013, 1305.0729.

[7] Sandip Singh,et al. Arithmeticity of certain symplectic hypergeometric groups , 2012, 1208.6460.

[8] P. Sarnak. Notes on Thin Matrix Groups , 2012, 1212.3525.

[9] H. Hornich. Vorlesungen über die hypergeometrische Funktion , 1934 .

[10] N. M. Katz. Another Look at the Dwork Family , 2009 .

[11] N. Yui,et al. Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds , 2006, math/0605675.