On compression of Bruhat-Tits buildings

Details On compression of Bruhat-Tits buildings On compression of Bruhat-Tits buildings

2004-10-09

arxiv.org/abs/math/0410242v1

Mathematics

Representation Theory

6 pages

Scientific paper

We obtain an analog of the compression of angles theorem in symmetric spaces for Bruhat--Tits buildings of the type $A$. More precisely, consider a $p$-adic linear space $V$ and the set $Lat(V)$ of all lattices in $V$. The complex distance in $Lat(V)$ is a complete system of invariants of a pair of points of $Lat(V)$ under the action of the complete linear group. An element of a Nazarov semigroup is a lattice in the duplicated linear space $V\oplus V$. We investigate behavior of the complex distance under the action of the Nazarov semigroup on the set $Lat(V)$.

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