A tropical view on Bruhat-Tits buildings and their compactifications

• Autorzy: Annette Werner
• Języki publikacji: EN

Abstrakty

EN

We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of its compactifications are described by tropical linear algebra. The compactifications we consider arise from algebraic representations of G. We show that the fan which is used to compactify an apartment in this theory is given by the weight polytope of the representation and that it is related to the tropicalization of the hypersurface given by the character of the representation.

Słowa kluczowe

EN

Bruhat-Tits buildings; Tropical geometry; Weight polytopes

Kategorie tematyczne

• 14T05: Tropical geometry
• 20G25: Linear algebraic groups over local fields and their integers
• 20E42: Groups with a B N -pair; buildings

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 2
• Strony: 390-402

Daty

wydano

2011-04-01

online

2011-02-18

Twórcy

autor

Annette Werner

• Goethe-Universität Frankfurt

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0005-3