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arXiv · 1011.6636

Ideal triangles in Euclidean buildings and branching to Levi subgroups

Thomas J. Haines·Michael Kapovich·John J. Millson
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Abstract

We introduce the notion of ideal triangle in the Bruhat-Tits building associated to a split group -- it is analogous to the usual notion of triangle, but one vertex is "at infinity" in a certain direction. We prove that the algebraic variety of based ideal triangles with prescribed side-lengths is naturally isomorphic to a suitable variety of genuine triangles. From theorems pertaining to genuine triangles, we deduce saturation theorems related to branching to Levi subgroups and to the constant term homomorphisms.

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BibTeXRIS

Thomas J. Haines, Michael Kapovich, John J. Millson. 2010-11-30. Ideal triangles in Euclidean buildings and branching to Levi subgroups. https://arxiv.org/abs/1011.6636

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