Description of unitary representations of the group of infinite 𝑝-adic integer matrices

Neretin, Yury

doi:10.1090/ert/577

Description of unitary representations of the group of infinite $p$-adic integer matrices
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by Yury A. Neretin

Represent. Theory 25 (2021), 606-643

DOI: https://doi.org/10.1090/ert/577

Published electronically: July 19, 2021

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Abstract:

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of infinite matrices over a residue ring modulo $p^k$. Irreducible representations of the latter group are induced from finite-dimensional representations of certain open subgroups.

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