On compression of Bruhat–Tits buildings

Consider an affine Bruhat–Tits building Latn of type $A_{n-1}$ and the complex distance in $\mathrm{Lat}_n$, i.e., the complete system of invariants of a pair of vertices of the building. An element of the Nazarov semigroup is a lattice in the duplicated $p$-adic space $\mathbb Q_p^n\oplus\mathbb Q_p^n$. We investigate the behavior of the complex distance with respect to the natural action of the Nazarov semigroup on the building. Bibliography: 18 titles.