Ideal triangles in Euclidean buildings and branching to Levi subgroups

Details Ideal triangles in Euclidean buildings and branching to Levi subgroups Ideal triangles in Euclidean buildings and branching to Levi subgroups

2010-11-30

arxiv.org/abs/1011.6636v1

Mathematics

Representation Theory

40 pages, 2 figures, 1 table

Scientific paper

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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