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Slow exponential growth representations of Sp(n, 1) at the edge of Cowling's strip

Slow exponential growth representations of Sp(n, 1) at the edge of Cowling's strip
Slow exponential growth representations of Sp(n, 1) at the edge of Cowling's strip
We obtain a slow exponential growth estimate for the spherical principal series representation rho_s of Lie group Sp(n, 1) at the edge (Re(s)=1) of Cowling's strip (|Re(s)|<1) on the Sobolev space H^alpha(G/P) when alpha is the critical value Q/2=2n+1. As a corollary, we obtain a slow exponential growth estimate for the homotopy rho_s (s in [0, 1]) of the spherical principal series which is required for the first author's program for proving the Baum--Connes conjecture with coefficients for Sp(n,1).
math.RT, math.FA
0379-4024
283-302
Julg, Pierre
dbfd88f4-51c1-43b5-937b-5c4d15095fc4
Nishikawa, Shintaro
3e8c8e9a-a181-4a7b-9cc6-a70e16177703
Julg, Pierre
dbfd88f4-51c1-43b5-937b-5c4d15095fc4
Nishikawa, Shintaro
3e8c8e9a-a181-4a7b-9cc6-a70e16177703

Julg, Pierre and Nishikawa, Shintaro (2024) Slow exponential growth representations of Sp(n, 1) at the edge of Cowling's strip. Journal of Operator Theory, 92 (1), 283-302. (doi:10.7900/jot.2022oct12.2437).

Record type: Article

Abstract

We obtain a slow exponential growth estimate for the spherical principal series representation rho_s of Lie group Sp(n, 1) at the edge (Re(s)=1) of Cowling's strip (|Re(s)|<1) on the Sobolev space H^alpha(G/P) when alpha is the critical value Q/2=2n+1. As a corollary, we obtain a slow exponential growth estimate for the homotopy rho_s (s in [0, 1]) of the spherical principal series which is required for the first author's program for proving the Baum--Connes conjecture with coefficients for Sp(n,1).

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2106.10536v2 - Accepted Manuscript
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Accepted/In Press date: 19 June 2021
Published date: 2024
Keywords: math.RT, math.FA

Identifiers

Local EPrints ID: 496701
URI: http://eprints.soton.ac.uk/id/eprint/496701
DOI: doi:10.7900/jot.2022oct12.2437
ISSN: 0379-4024
PURE UUID: 0bb9cb00-e16e-421d-9335-123a5e80003f
ORCID for Shintaro Nishikawa: ORCID iD orcid.org/0000-0003-4593-3069

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Date deposited: 07 Jan 2025 22:03
Last modified: 17 Jul 2025 02:25

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Author: Pierre Julg
Author: Shintaro Nishikawa ORCID iD

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