Abstract
In this paper we give a complete invariant of the action of on the Euclidean building $\mathcal B_e$, where is a discrete valuation field. We then use this invariant to give a natural metric on the resulting quotient space. In the special case of the torus acting on the tree $\mathcal B_e$, we obtain an algorithm for calculating the distance of any vertex in the tree to any fixed apartment.
Citation
Jonathan Needleman. "Maximal Levi subgroups acting on the Euclidean building of $\mathrm{GL}_n(F)$." Innov. Incidence Geom. 12 7 - 19, 2011. https://doi.org/10.2140/iig.2011.12.7
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