Gross--Prasad periods for reducible representations
Representation Theory
2021-11-10 v2 Number Theory
Abstract
We study GL_2(F)-invariant periods on representations of GL_2(A), where F is a nonarchimedean local field and 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 at most 1, and is non-zero when a certain epsilon-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 x F x F.
Cite
@article{arxiv.2103.14683,
title = {Gross--Prasad periods for reducible representations},
author = {David Loeffler},
journal= {arXiv preprint arXiv:2103.14683},
year = {2021}
}
Comments
Revised version, to appear in Forum Mathematicum