Groups, Geometry, and Dynamics


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Volume 2, Issue 3, 2008, pp. 405–480
DOI: 10.4171/GGD/46

Published online: 2008-09-30

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

Michael Kapovich[1] and John J. Millson[2]

(1) University of California at Davis, United States
(2) University of Maryland, College Park, USA

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 reductive Lie groups and to spherical Hecke rings associated with split nonarchimedean reductive Lie groups. Our main application is a generalization of the saturation theorem of Knutson and Tao for SLn to other complex semisimple Lie groups.

Keywords: Euclidean buildings, LS path model, saturation theorem

Kapovich Michael, Millson John: A path model for geodesics in Euclidean buildings and its applications to representation theory. Groups Geom. Dyn. 2 (2008), 405-480. doi: 10.4171/GGD/46