Skip to main content
MathOverflow

Return to Question

+ top level tag (nt.)
Source Link
Myshkin
Myshkin
  • 17.6k
  • 5
  • 71
  • 137

Take $F$ a number field, $\pi$ a cuspidal automorphic representation of $GL(3, \mathbb{A}_F).$ Suppose $\pi \cong \pi\otimes \chi.$ Comparing central characters we see that $\chi$ must be cubic.

Now suppose $\chi$ is a cubic character of $\mathbb{A}_F^\times$. Is it known how to construct $\pi$ such that $\pi \cong \pi\otimes \chi$ (or whether it is possible to do so)?

Take $F$ a number field, $\pi$ a cuspidal automorphic representation of $GL(3, \mathbb{A}_F).$ Suppose $\pi \cong \pi\otimes \chi.$ Comparing central characters we see that $\chi$ must be cubic.

Now suppose $\chi$ is a cubic character of $\mathbb{A}_F^\times$ Is it known how to construct $\pi$ such that $\pi \cong \pi\otimes \chi$ (or whether it is possible to do so)?

Take $F$ a number field, $\pi$ a cuspidal automorphic representation of $GL(3, \mathbb{A}_F).$ Suppose $\pi \cong \pi\otimes \chi.$ Comparing central characters we see that $\chi$ must be cubic.

Now suppose $\chi$ is a cubic character of $\mathbb{A}_F^\times$. Is it known how to construct $\pi$ such that $\pi \cong \pi\otimes \chi$ (or whether it is possible to do so)?

Source Link
Joseph Hundley
Joseph Hundley
  • 590
  • 2
  • 13

Is there a known construction of Cuspidal representations of GL(3) isomorphic to their own twist?

Take $F$ a number field, $\pi$ a cuspidal automorphic representation of $GL(3, \mathbb{A}_F).$ Suppose $\pi \cong \pi\otimes \chi.$ Comparing central characters we see that $\chi$ must be cubic.

Now suppose $\chi$ is a cubic character of $\mathbb{A}_F^\times$ Is it known how to construct $\pi$ such that $\pi \cong \pi\otimes \chi$ (or whether it is possible to do so)?