Timeline for $\mathrm{GL}(n, \mathbb{Z})$-equivariant maps on $\mathrm{GL}(n, \mathbb{R})$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 21, 2023 at 13:37 | comment | added | David E Speyer | What kind of description would satisfy you? If $n=1$, you are talking about all odd functions $\mathbb{R}_{\neq 0} \to \mathbb{R}_{\neq 0}$. | |
| Jun 21, 2023 at 12:25 | comment | added | YCor | The ones equivariant by all of GL(n,R) are the left multiplications. For what you like, writing $f(g)=s(g)g$, we see that $s(g)=s(gh)$ for all $h\in$GL(n,Z). Hence, the answer is the maps $f(g)=s(g)g$ for such maps $s$ (i.e., factoring through maps GL(n,R)/GL(n,Z)$\to$ GL(n,R). If you require the map to be continuous, this means that $s$ is continuous. | |
| Jun 21, 2023 at 12:22 | history | edited | YCor | CC BY-SA 4.0 |
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| Jun 21, 2023 at 11:21 | history | asked | gm01 | CC BY-SA 4.0 |