Λ-buildings associated to quasi-split groups over Λ-valued fields

2020/01/06 by Hébert, Auguste, Izquierdo, Diego, Loisel, Benoit
#20E42 #20G15 #51E24 #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2001.01542

Abstract

Let G be a quasi-split reductive group and \mathbbK be a Henselian field equipped with a valuation ω:\mathbbK^×→ Λ, where Λ is a non-zero totally ordered abelian group. In 1972, Bruhat and Tits constructed a building on which the group G(\mathbbK) acts provided that Λ is a subgroup of ℝ. In this paper, we deal with the general case where there are no assumptions on Λ and we construct a set on which G(\mathbbK) acts. We then prove that it is a Λ-building, in the sense of Bennett.

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