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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Characters of irreducible unitary representations of $\operatorname {U}(n, n+1)$ via double lifting from $\operatorname {U}(1)$
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by Allan Merino PDF
Represent. Theory 26 (2022), 325-369 Request permission


In this paper, we obtained character formulas of irreducible unitary representations of $U(n, n+1)$ by using Howe’s correspondence and the Cauchy–Harish-Chandra integral. The representations of $U(n, n+1)$ we are dealing with are obtained from a double lifting of a representation of $U(1)$ via the dual pairs $(U(1), U(1, 1))$ and $(U(1, 1), U(n, n+1))$.
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Additional Information
  • Allan Merino
  • Affiliation: Department of Mathematics, National University of Singapore, 21 Lower Kent Ridge Road, Singapore 119077
  • Address at time of publication: Department of Mathematics and Statistics, University of Ottawa, STEM Complex, 150 Louis-Pasteur Pvt., Ottawa, Ontario, K1N6N5, Canada
  • MR Author ID: 1393076
  • ORCID: 0000-0001-8545-9803
  • Email:
  • Received by editor(s): March 17, 2021
  • Received by editor(s) in revised form: September 14, 2021
  • Published electronically: March 23, 2022
  • Additional Notes: The author was supported by the MOE-NUS AcRF Tier 1 grants R-146-000-261-114 and R-146-000-302-114.
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 325-369
  • MSC (2020): Primary 22E45; Secondary 22E46, 22E30
  • DOI:
  • MathSciNet review: 4398474