Timeline for Haar measure on $\mathrm{SL}_3(\mathbb{Z}) \backslash \mathrm{SL}_3(\mathbb{R}) / \mathrm{SO}_3(\mathbb{R})$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| May 17, 2019 at 17:08 | comment | added | LSpice | How do you single out a (family of) measure on this space, which does not carry any obvious group action, as 'Haar measure'? Do you just mean the measure for which $$\int_{\operatorname{SL}_3(\mathbb R)} f(x)\mathrm dx = \int_{\operatorname{SL}_3(\mathbb Z)\backslash{\operatorname{SL}_3(\mathbb R)}/{\operatorname{SO}_3(\mathbb R)}} \Bigl(\int_{\operatorname{SL}_3(\mathbb Z)x{\operatorname{SO}_3(\mathbb R)}} f(y)\mathrm dy\Bigr)\mathrm dx?$$ | |
| Feb 20, 2018 at 6:59 | history | edited | user120980 | CC BY-SA 3.0 |
edited body
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| Feb 20, 2018 at 6:58 | comment | added | user120980 | It's edited, thanks for noticing and explaining. | |
| Feb 20, 2018 at 6:52 | vote | accept | user120980 | ||
| Feb 19, 2018 at 13:42 | comment | added | YCor | In general for double coset spaces $\Gamma\backslash G/K$ ($G$ unimodular, $K$ compact, $\Gamma$ discrete) the main step is to describe a $G$-invariant Radon measure on $G/K$, and then modding out by $\Gamma$ yields the given space ($G/K$ already known the local form of the measure). The main difficulty is not to describe the measure, but rather describe a fundamental domain. There exists a large literature on this, starting with Siegel. See Peter's answer. | |
| Feb 19, 2018 at 13:35 | comment | added | YCor | It's: "Iwasawa" | |
| Feb 19, 2018 at 11:39 | answer | added | Peter Humphries | timeline score: 14 | |
| Feb 19, 2018 at 11:18 | history | edited | Peter Humphries | CC BY-SA 3.0 |
added 98 characters in body; edited tags; edited title
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| Feb 19, 2018 at 7:06 | review | First posts | |||
| Feb 19, 2018 at 7:12 | |||||
| Feb 19, 2018 at 7:05 | history | asked | user120980 | CC BY-SA 3.0 |