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AlgSoul
AlgSoul
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Any finite dimensional admissible(smooth) irreducible representation of GL(2,Q_p) is 1-dim

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AlgSoul
AlgSoul
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Just like the title. I want a simple proof of the statment in the title. $\mathbb{Q}_p$ is the p-adic field. I wonder which module (or vector space) will be chosen as the space for the representation. Is this statement true for arbitarily module/vector space? Thanks!

p.s. I cannot understand the comment by bcnrd...plz explain it anyone?

Just like the title. I want a simple proof of the statment in the title. $\mathbb{Q}_p$ is the p-adic field. I wonder which module (or vector space) will be chosen as the space for the representation. Is this statement true for arbitarily module/vector space? Thanks!

p.s. I cannot understand the comment by bcnrd...plz explain it anyone?

Just like the title. I want a simple proof of the statment in the title. $\mathbb{Q}_p$ is the p-adic field. I wonder which module (or vector space) will be chosen as the space for the representation. Is this statement true for arbitarily module/vector space? Thanks!

added 74 characters in body; edited title
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AlgSoul
AlgSoul
  • 53
  • 4

The Any finite dimensional admissible irreducible representation of GL(2,Q_p) is 1-dim

Just like the title. I want a simple proof of the statment in the title. $\mathbb{Q}_p$ is the p-adic field. I wonder which module (or vector space) will be chosen as the space for the representation. Is this statement true for arbitarily module/vector space? Thanks!

p.s. I cannot understand the comment by bcnrd...plz explain it anyone?

The finite dimensional admissible irreducible representation of GL(2,Q_p) is 1-dim

Just like the title. I want a simple proof of the statment in the title. $\mathbb{Q}_p$ is the p-adic field. I wonder which module (or vector space) will be chosen as the space for the representation. Is this statement true for arbitarily module/vector space? Thanks!

Any finite dimensional admissible irreducible representation of GL(2,Q_p) is 1-dim

Just like the title. I want a simple proof of the statment in the title. $\mathbb{Q}_p$ is the p-adic field. I wonder which module (or vector space) will be chosen as the space for the representation. Is this statement true for arbitarily module/vector space? Thanks!

p.s. I cannot understand the comment by bcnrd...plz explain it anyone?

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AlgSoul
AlgSoul
  • 53
  • 4