  For the space $Lat_n$ 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 $Lat_n$. We obtain conditions of positive definiteness of
these kernels and explicit Plancherel formula.
