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


Author: Yury A. Neretin
Journal: Represent. Theory 25 (2021), 606-643
MSC (2020): Primary 22E50; Secondary 22E66, 20M18, 18B99
DOI: https://doi.org/10.1090/ert/577
Published electronically: July 19, 2021
MathSciNet review: 4287865
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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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Additional Information

Yury A. Neretin
Affiliation: Pauli Institute, Vienna, Austria; Institute for Theoretical Experimental Physics, Moscow, Russia; Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia; and Institute for Information Transmission Problems, Moscow, Russia
Address at time of publication: Department of Mathematics, University of Vienna, Vienna, Austria
MR Author ID: 210026

Received by editor(s): September 22, 2019
Received by editor(s) in revised form: April 14, 2021
Published electronically: July 19, 2021
Additional Notes: This work was supported by the grants FWF, P28421, P31591
Article copyright: © Copyright 2021 American Mathematical Society