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Beta-function of Bruhat--Tits buildings and deformation of $l_2$ on the space of lattices

Yurii A. Neretin
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Abstract

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.

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Yurii A. Neretin. 2003-04-14. Beta-function of Bruhat--Tits buildings and deformation of $l_2$ on the space of lattices. https://doi.org/10.4213/sm786,10.1070/sm2003v194n12abeh000786

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