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GENERATORS OF THE EISENSTEIN–PICARD MODULAR GROUP

Part of: Complex spaces with a group of automorphisms Automorphic functions

Published online by Cambridge University Press:  07 February 2012

JIEYAN WANG ,
YINGQING XIAO  and
BAOHUA XIE
JIEYAN WANG
Affiliation:
College of Mathematics and Economics, Hunan University, Changsha 410082, PR China (email: [email protected])
YINGQING XIAO*
Affiliation:
College of Mathematics and Economics, Hunan University, Changsha 410082, PR China (email: [email protected])
BAOHUA XIE
Affiliation:
College of Mathematics and Economics, Hunan University, Changsha 410082, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We prove that the Eisenstein–Picard modular group SU(2,1;ℤ[ω3]) can be generated by four given transformations.

Keywords

complex hyperbolic spacePicard modular group

MSC classification

Secondary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 3 , December 2011 , pp. 421 - 429
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

This work was partially supported by The National Natural Science Foundation of China (No. 11071059). Xie was also supported by Hunan University (No. 531107040021).

References

[1]Bao, L., Colonello, C., Kleinschmidt, A., Nillson, B. and Persson, D., ‘Instanton correction to the universal hypermultiplet and automorphic forms on SU(2,1)’, Commun. Numer. Theory Phys. 4 (2010), 187–266.CrossRefGoogle Scholar
[2]Falbel, E., Francsics, G., Lax, P. D. and Parker, J. R., ‘Generators of a Picard modular group in two complex dimensions’, Proc. Amer. Math. Soc. 139 (2011), 2439–2447.CrossRefGoogle Scholar
[3]Falbel, E., Francsics, G. and Parker, J. R., ‘The geometry of the Gauss–Picard modular group’, Math. Ann. 349 (2011), 459–508.CrossRefGoogle Scholar
[4]Falbel, E. and Parker, J. R., ‘The geometry of the Eisenstein–Picard modular group’, Duke Math. J. 131 (2006), 249–289.CrossRefGoogle Scholar
[5]Francsics, G. and Lax, P., ‘A semi-explicit fundamental domain for a Picard modular group in complex hyperbolic space’, Contemp. Math. 238 (2005), 211–226.CrossRefGoogle Scholar
[6]Francsics, G. and Lax, P., ‘An explicit fundamental domain for a Picard modular group in complex hyperbolic space’, Preprint, 2005, pp. 1–25, arXiv:math/0509708.CrossRefGoogle Scholar
[7]Goldman, W. M., Complex Hyperbolic Geometry (Oxford University Press, Oxford, 1999).CrossRefGoogle Scholar
[8]Hardy, G. H. and Wright, E. M., An Introduction to the Theory of Numbers (Oxford University Press, Oxford, 1954).Google Scholar
[9]Holzapfel, R.-P., ‘Invaiants of arithmetric ball quotient sufraces’, Math. Nachr. 103 (1981), 117–153.CrossRefGoogle Scholar
[10]Parker, J. R., Notes on Complex Hyperbolic Geometry (Preliminary version, 2003).Google Scholar
[11]Zhao, T., ‘Generators for the Euclidean Picard modular groups’, Trans. Amer. Math. Soc., to appear.Google Scholar