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Characters of irreducible unitary representations of $\operatorname {U}(n, n+1)$ via double lifting from $\operatorname {U}(1)$

Author: Allan Merino
Journal: Represent. Theory 26 (2022), 325-369
MSC (2020): Primary 22E45; Secondary 22E46, 22E30
Published electronically: March 23, 2022
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Abstract: 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

Keywords: Howe correspondence, characters, Cauchy–Harish-Chandra integral, orbital integrals
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.
Article copyright: © Copyright 2022 American Mathematical Society