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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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
Published electronically: July 19, 2021


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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Bibliographic 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
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 606-643
  • MSC (2020): Primary 22E50; Secondary 22E66, 20M18, 18B99
  • DOI:
  • MathSciNet review: 4287865