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• W3103237761 abstract "In our previous paper Bruhat-Tits theory from Berkovich's point of view. I ? Realizations and compactifications of buildings, we investigated realizations of the Bruhat-Tits building B(G,k) of a connected and reductive linear algebraic group G over a non-Archimedean field k in the framework of Berkovich's non-Archimedean analytic geometry, and we studied in detail the compactifications of the building which arise from this point of view. In this paper, we give a representation theoretic flavor to these compactifications, following Satake's original constructions for Riemannian symmetric spaces. We first prove that Berkovich compactifications of a building coincide with the compactifications previously introduced by the third named author and obtained by a gluing procedure. Then we show how to recover them from an absolutely irreducible linear representation of G by embedding B(G,k) in the building of the general linear group of the representation space, compactified in a suitable way. Existence of such an embedding is a special case of Landvogt's general results on functoriality of buildings, but we also give another natural construction of an equivariant embedding, which relies decisively on Berkovich geometry." @default.
• W3103237761 created "2020-11-23" @default.
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• W3103237761 date "2011-12-13" @default.
• W3103237761 modified "2023-09-27" @default.
• W3103237761 title "Bruhat–Tits theory from Berkovich's point of view. II Satake compactifications of buildings" @default.
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• W3103237761 doi "https://doi.org/10.1017/s1474748011000168" @default.
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