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The generalized linear period
Hengfei Lu
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Let F be a non-archimedean local field of characteristic zero. We study the linear period problem for the pair (G,H_(p,p+1))=(GL₂ₚ₊₁(F), GLₚ(F)×GLₚ₊₁(F)) and we prove that any bi-(H_(p,p+1),μ)-invariant generalized function on G is invariant under the matrix transpose when \mu is a good character. We also show that any P∩H_(p,p+1)-invariant linear functional on an H_(p,p+1)-distinguished irreducible smooth representation of G is also H_(p,p+1)-invariant when F is nonarchimedean, where P is a standard mirabolic subgroup of G with last row vector (0,⋯,0,1).
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