A path model for geodesics in Euclidean buildings and its applications to representation theory

Details A path model for geodesics in Euclidean buildings and its applications to representation theory A path model for geodesics in Euclidean buildings and its applications to representation theory

2004-11-08

arxiv.org/abs/math/0411182v2

Mathematics

Representation Theory

72 pages, 10 figures

Scientific paper

In this paper we give a combinatorial characterization of projections of geodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex semisimple Lie groups and to spherical Hecke rings associated with nonarchimedean reductive Lie groups. Our main application is a generalization of the saturation theorem of Knutson and Tao for SL(n) to other complex semisimple Lie groups.

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