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Monty
Monty
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I am wondering why the first well known example of non-tempered irreducible admissible representation of $p$-adic group $U(n)$ should be $U(3)$. Because, Gelbart and Rogawski suggested the non-tempered representation of $U(3)$ using the theta lift.

I know all irreducible representation of $U(1)$ should be tempered because $U(1)$ is compact. But why isn't there known example for the non-tempered representation of $U(2)$? I think it should be there.

I am wondering why the first well known example of irreducible admissible representation of $p$-adic group $U(n)$ should be $U(3)$. Because, Gelbart and Rogawski suggested the non-tempered representation of $U(3)$ using the theta lift.

I know all irreducible representation of $U(1)$ should be tempered because $U(1)$ is compact. But why isn't there known example for the non-tempered representation of $U(2)$? I think it should be there.

I am wondering why the first well known example of non-tempered irreducible admissible representation of $p$-adic group $U(n)$ should be $U(3)$. Because, Gelbart and Rogawski suggested the non-tempered representation of $U(3)$ using the theta lift.

I know all irreducible representation of $U(1)$ should be tempered because $U(1)$ is compact. But why isn't there known example for the non-tempered representation of $U(2)$? I think it should be there.

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Monty
Monty
  • 1.8k
  • 9
  • 9

Is there a non-tempered representation of U(2)?

I am wondering why the first well known example of irreducible admissible representation of $p$-adic group $U(n)$ should be $U(3)$. Because, Gelbart and Rogawski suggested the non-tempered representation of $U(3)$ using the theta lift.

I know all irreducible representation of $U(1)$ should be tempered because $U(1)$ is compact. But why isn't there known example for the non-tempered representation of $U(2)$? I think it should be there.