Slow exponential growth representations of Sp(n, 1) at the edge of Cowling's strip
Abstract
We obtain a slow exponential growth estimate for the spherical principal series representation rhos of Lie group Sp(n, 1) at the edge (Re(s)=1) of Cowling's strip (|Re(s)|<1) on the Sobolev space Halpha(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 rhos (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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