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DISTANCES ON A MASURE

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Abstract

A masure (also known as an affine ordered hovel) is a generalization of the Bruhat-Tits building that is associated with a split Kac-Moody group G over a nonarchimedean local field. This is a union of affine spaces called apartments. When G is a reductive group, is a building and there is a G-invariant distance inducing a norm on each apartment. In this paper, we study distances on inducing the affine topology on each apartment. We construct distances such that each element of G is a continuous automorphism of and we study their properties (completeness, local compactness, …).

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  1. Université de Lorraine, Institut Élie Cartan de Lorraine, UMR 7502, F-54000, Nancy, France

    AUGUSTE HÉBERT

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  1. AUGUSTE HÉBERT
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Correspondence to AUGUSTE HÉBERT.

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HÉBERT, A. DISTANCES ON A MASURE. Transformation Groups 26, 1331–1363 (2021). https://doi.org/10.1007/s00031-021-09674-9

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  • DOI: https://doi.org/10.1007/s00031-021-09674-9

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