Abstract
Consider an affine Bruhat-Tits building Lat n of type An−1 and the complex distance in 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 ℚ p n ⊕ 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.
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