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Abstract: We relate some features of Bruhat-Tits buildings and their compactificationsto tropical geometry. If G is a semisimple group over a suitablenon-Archimedean field, the stabilizers of points in the Bruhat-Tits building ofG and in some of its compactifications are described by tropical linearalgebra. The compactifications we consider arise from algebraic representationsof G. We show that the fan which is used to compactify an apartment in thistheory is given by the weight polytope of the representation and that it isrelated to the tropicalization of the hypersurface given by the character ofthe representation.



Author: Annette Werner

Source: https://arxiv.org/







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