Generators of a Picard modular group in two complex dimensions

Falbel, Elisha; Francsics, Gábor; Lax, Peter; Parker, John

doi:10.1090/S0002-9939-2010-10653-6

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Generators of a Picard modular group in two complex dimensions

Authors: Elisha Falbel, Gábor Francsics, Peter D. Lax and John R. Parker
Journal: Proc. Amer. Math. Soc. 139 (2011), 2439-2447
MSC (2010): Primary 32M05, 22E40; Secondary 32M15
Posted: November 30, 2010
MathSciNet review: 2784810
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Abstract: The goal of the article is to prove that four explicitly given transformations, two Heisenberg translations, a rotation and an involution generate the Picard modular group with Gaussian integers acting on the two dimensional complex hyperbolic space. The result answers positively a question raised by A. Kleinschmidt and D. Persson.

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Additional Information

Elisha Falbel
Affiliation: Institut de Mathématiques, Université Pierre et Marie Curie, 4 Place Jussieu, Paris, France
Email: falbel@math.jussieu.fr

Gábor Francsics
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: francsics@math.msu.edu

Peter D. Lax
Affiliation: Courant Institute, New York University, 251 Mercer Street, New York, New York 10012-1185
Email: lax@courant.nyu.edu

John R. Parker
Affiliation: Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, United Kingdom
Email: j.r.parker@durham.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10653-6
PII: S 0002-9939(2010)10653-6
Keywords: Complex hyperbolic space, Picard modular groups
Received by editor(s): October 8, 2009
Received by editor(s) in revised form: June 17, 2010
Posted: November 30, 2010
Additional Notes: The second author is grateful for the hospitality of the Mathematical Sciences Research Institute at Berkeley and the Rényi Mathematical Institute, Budapest.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2010 American Mathematical Society

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