N ov 2 00 8 Maximal Levi Subgroups Acting on the Euclidean Building of GL n ( F ) Jonathan Needleman
نویسنده
چکیده
In this paper we give a complete invariant of the action of GL n (F)× GL m (F) on the Euclidean building B e GL n+m (F), where F is a non-archimedian 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 B e GL 2 (F) this gives a method for calculating the distance of any vertex to any fixed apartment.
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