A Convexity property for the SO(2,C)-double coset decomposition of SL(2,C) and applications to spherical functions

Details A Convexity property for the SO(2,C)-double coset decomposition of SL(2,C) and applications to spherical functions A Convexity property for the SO(2,C)-double coset decomposition of SL(2,C) and applications to spherical functions

2002-08-27

arxiv.org/abs/math/0208215v2

Math. Z. 247(2), 303-318 (2004)

Mathematics

Representation Theory

15 pages, 2 figures. Simpler geometric proofs of the results in Section 3 are given. To appear in Math. Z

Scientific paper

We make a fine study of the SO(2,C)-double coset decomposition in SL(2,C) and
give a full description of the intersection of the various cells with the
complex crown Xi of SL(2,R)/SO(2). A non-linear convexity theorem is proved and
applications to analytically continued spherical functions are given.

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