Polygons in Buildings and their Refined Side Lengths |
| |
Authors: | Michael Kapovich Bernhard Leeb John J. Millson |
| |
Affiliation: | 1. Department of Mathematics, University of California, Davis, CA, 95616, USA 2. Mathematisches Institut, Universit?t München, Theresienstrasse 39, D-80333, München, Germany 3. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA
|
| |
Abstract: | As in a symmetric space of noncompact type, one can associate to an oriented geodesic segment in a Euclidean building a vector valued length in the Euclidean Weyl chamber Δ euc . In addition to the metric length it contains information on the direction of the segment. In this paper we study restrictions on the Δ euc -valued side lengths of polygons in Euclidean buildings. The main result is that for thick Euclidean buildings X the set Pn(X){mathcal{P}n(X)} of possible Δ euc -valued side lengths of oriented n-gons depends only on the associated spherical Coxeter complex. We show moreover that it coincides with the space of Δ euc -valued weights of semistable weighted configurations on the Tits boundary ∂ Tits X. The side lengths of polygons in symmetric spaces of noncompact type are studied in the related paper [KLM1]. Applications of the geometric results in both papers to algebraic group theory are given in [KLM2]. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|