Affiliation:
1. Warwick Mathematics Institute , University of Warwick , Coventry CV4 7AL , United Kingdom
Abstract
Abstract
We study
GL
2
(
F
)
{\operatorname{GL}_{2}(F)}
-invariant periods on representations of
GL
2
(
A
)
{\operatorname{GL}_{2}(A)}
, where F is a non-archimedean local field and
A
/
F
{A/F}
a product of field extensions of total degree 3. For irreducible representations, a theorem of Prasad shows that the space of such periods has dimension
⩽
1
{\leqslant 1}
, and is non-zero when a certain ε-factor condition holds. We give an extension of this result to a certain class of reducible representations (of Whittaker type), extending results of Harris–Scholl when A is the split algebra
F
×
F
×
F
{F\times F\times F}
.
Subject
Applied Mathematics,General Mathematics
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Cited by
1 articles.
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