Timeline for When does Haar measure decompose into products of such?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2021 at 0:07 | answer | added | Alex Kontorovich | timeline score: 2 | |
| Apr 12, 2021 at 23:23 | comment | added | Yemon Choi | Without thinking at all deeply about this, my suspicion is that in the first example one is really getting a product of Haar measures on P and K where P=NA; and then it so happens that the parabolic P has a nice semidirect product decomposition. I also suspect that for this particular example the compactness of K is important, but this is just a tentative hunch and I could easily be shown wrong here | |
| Apr 12, 2021 at 20:42 | comment | added | LSpice | But, to the general question, I suspect that, absent the obvious case where conjugation by $H$ acts by measure-preserving isomorphisms on $K$, or vice versa, there is no very good general answer for when this happens. | |
| Apr 12, 2021 at 20:40 | comment | added | LSpice | I'm not sure what you mean by writing $\mathrm dg = \mathrm dx(\mathrm dy/y^2)\mathrm dk$ and $\mathrm dg = \mathrm dn\,\mathrm da\,\mathrm dk$; $\mathrm da$ is $\mathrm dy/y$, not $\mathrm dy/y^2$ (assuming $a = \begin{pmatrix} y \\ & y^{-1} \end{pmatrix}$). | |
| Apr 12, 2021 at 20:30 | review | First posts | |||
| Apr 13, 2021 at 5:47 | |||||
| Apr 12, 2021 at 20:29 | history | asked | Alex Kontorovich | CC BY-SA 4.0 |