Analysis on the crown domain

Details Analysis on the crown domain Analysis on the crown domain

2006-06-09

arxiv.org/abs/math/0606213v2

GAFA, Geom. funct. anal. 18 (2008), 1326-1421

Mathematics

Representation Theory

Revised version. 103 pages. To appear in GAFA

Scientific paper

In this paper one finds:1) A simple combinatorical description of the distinguished boundary of the crown domain in terms of the affine Weyl group; 2) Optimal upper and lower bounds for holomorphically extended spherical functions; 3) First progress on how to attach complex invariants to irreducible representations; 4) A new unipotent model for the crown domain; 5) Optimal bounds for the exponential decay of cuspidal automorphic forms.

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