SOME RESULTS ON THE LOCALLY SYMMETRIC STRUCTURE OF HALF UPPER SPACES
Abstract
Locally symmetric spaces play an important part in differential geometryand arise from many different areas such as topology, number theory, representa-tion theory, algebraic geometry,...The typical important class consists of quotientsof symmetric spaces by arithmetic groups, for example, the moduli space of ellipticcurves is the quotient of the upper half plane H2 by SL(2; Z).In this paper, firstly, we study the symmetric structure of the upper half space H3and the relation with the symmetric space SL(2;C)=SU(2): Then we study the locallysymmetric space SL(2;Z + iZ)nH3 = SL(2;Z + iZ)nSL(2;C)=SU(2) based on theaction of the discrete group SL(2; Z + iZ) on H3:References
E.P. Van den Ban, Lie groups, Lecture Notes in Mathematics, MRI, University of
Utrecht, Holland, 2003.
E.P. Van den Ban - H. Schlichtkrull, Harmonic analysis on reductive symmetric
spaces, Progress in Math., 201, Birkhauser Verlag, Basel, 2001, 565-582.
B.Conrad, K.Rubin, Arithmetic algebraic geometry, IAS/Park City Math Series,
vol. 9, AMS, 2001.
L.Ji, An introduction to symmetric spaces and their compactifications, University
of Michigan, Ann Arbor, MI 48109, 2001.
L.Ji, Lectures on locally symmetric spaces and arithmetic groups, University of
Michigan, Ann Arbor, MI 48109, 2004.
Published
2013-09-26
Issue
Section
Khoa học Tự Nhiên
