Timeline for Conceptual explanation for failure of Kazhdan's property (T) for most rank 1 groups

10 events

when toggle format	what		by	license	comment
Jun 13 at 17:15	history	edited	cxrlo	CC BY-SA 4.0	edited title
Jun 13 at 17:15	comment	added	cxrlo		Thank you. I actually knew that, and the title was therefore quite misleading. I edited it appropiately.
Jun 13 at 16:28	comment	added	YCor		@MoisheKohan ah indeed. To clarify (to OP): some of the noncompact rank 1 groups have Kazhdan's Property T, but the proof is different (and harder). The first proof is due to Kostant.
Jun 13 at 16:06	comment	added	Moishe Kohan		@YCor: Of course. I was referring to the title question.
Jun 13 at 16:02	comment	added	YCor		@MoisheKohan the proof definitely fails for all rank 1 groups. The proof of Property T for $\mathrm{Sp}(n,1)$ is very different.
Jun 13 at 14:52	comment	added	Moishe Kohan		It does not even fail for all rank 1 groups, just for "most."
Jun 13 at 14:16	comment	added	YCor		Indeed, there is no semidirect product inside ($\mathrm{SL}_2(\mathbf{R})\ltimes\mathbf{R}^2$ in rank one groups. These play an essential role in the proofs (by Harpe-Valette / Bekka-Harpe-Valette and most others).
Jun 13 at 13:49	history	edited	cxrlo	CC BY-SA 4.0	edited title
S Jun 13 at 13:40	review	First questions
Jun 13 at 13:41
S Jun 13 at 13:40	history	asked	cxrlo	CC BY-SA 4.0