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We introduce the notion of ideal triangle in the Bruhat-Tits buildingassociated 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 thealgebraic variety of based ideal triangles with prescribed side-lengths isnaturally isomorphic to a suitable variety of genuine triangles. From theoremspertaining to genuine triangles, we deduce saturation theorems related tobranching to Levi subgroups and to the constant term homomorphisms.

Ideal triangles in Euclidean buildings and branching to Levi subgroups