A Convexity property for the SO(2,C)-double coset decomposition of SL(2,C) and applications to spherical functions
Abstract
Description
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.
15 pages, 2 figures. Simpler geometric proofs of the results in Section 3 are given. To appear in Math. Z
15 pages, 2 figures. Simpler geometric proofs of the results in Section 3 are given. To appear in Math. Z