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Paul Broussous
Paul Broussous
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Cooler Panda
Cooler Panda
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$Hom_G(C_c^{\infty}(G),\pi)=\cong Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C}) ?$

$G$ is an p-adic group, and $\pi$ is an irreducible representation of $G$, then do we naturally have $Hom_G(C_c^{\infty}(G),\pi)= Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C})$$Hom_G(C_c^{\infty}(G),\pi)\cong Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C})$? I think it is true, but I do not have found the detailed proof.

$Hom_G(C_c^{\infty}(G),\pi)= Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C}) ?$

$G$ is an p-adic group, and $\pi$ is an irreducible representation of $G$, then do we have $Hom_G(C_c^{\infty}(G),\pi)= Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C})$? I think it is true, but I do not have found the detailed proof.

$Hom_G(C_c^{\infty}(G),\pi)\cong Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C}) ?$

$G$ is an p-adic group, and $\pi$ is an irreducible representation of $G$, then do we naturally have $Hom_G(C_c^{\infty}(G),\pi)\cong Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C})$? I think it is true, but I do not have found the detailed proof.

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Cooler Panda
Cooler Panda
  • 467
  • 2
  • 8

$Hom_G(C_c^{\infty}(G),\pi)= Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C}) ?$

$G$ is an p-adic group, and $\pi$ is an irreducible representation of $G$, then do we have $Hom_G(C_c^{\infty}(G),\pi)= Hom_{\mathbb{C}}(\pi^{\vee},\mathbb{C})$? I think it is true, but I do not have found the detailed proof.