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Jun 11, 2015 at 16:15 comment added m07kl @YCor: The answer is yes. unipotent p -adic groups are all CCR, in particular type I. See Theorem 4 "Decomposition of Unitary Representations Defined by Discrete Subgroups of Nilpotent Groups" by Calvin C. Moore jstor.org/stable/1970567?seq=1#page_scan_tab_contents
May 16, 2015 at 9:19 comment added YCor The first question would be whether unipotent $p$-adic groups are all of type I.
May 16, 2015 at 1:44 history answered David Vogan CC BY-SA 3.0