Beta-function of Bruhat--Tits buildings and deformation of l₂ on the space of lattices

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For the space Latₙ of all the lattices in a p-adic n-dimensional linear space we obtain an analog of matrix beta-functions; this beta-function has a degeneration to the Tamagawa zeta-function. We propose an analog of Berezin kernels for Latₙ. We obtain conditions of positive definiteness of these kernels and explicit Plancherel formula.