Timeline for $Hom_G(C_c^{\infty}(G),\pi)\cong Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C}) ?$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 8, 2019 at 1:42 | comment | added | Cooler Panda | @LSpice Very helpful! | |
| Jan 8, 2019 at 1:41 | vote | accept | Cooler Panda | ||
| Jan 7, 2019 at 22:40 | comment | added | LSpice | With the inverse map given by $S \mapsto \bigl([g K] \mapsto (v^\vee \mapsto \int_K g k S(v^\vee)\,\mathrm d\mu(k))\bigr)$ for all $g \in G$ and all compact open subgroups $K$, where we have identified $\pi$ with its double contragredient. | |
| Jan 7, 2019 at 22:36 | comment | added | LSpice | Concretely, I think that the isomorphism is $T \mapsto (v^\vee \mapsto \lim_{K \downarrow \{1\}} v^\vee(T[K]))$, where $K$ runs over compact, open subgroups, and $T[K]$ is the value of $T$ at the characteristic function of the identity. | |
| Jan 7, 2019 at 22:32 | history | edited | LSpice | CC BY-SA 4.0 |
Missing subscript $G$ and ${\rm…}$ -> $\mathrm{…}$
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| Jan 7, 2019 at 20:11 | history | answered | Paul Broussous | CC BY-SA 4.0 |