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arXiv · 2103.14683

Gross--Prasad periods for reducible representations

David Loeffler
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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.

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BibTeXRIS

David Loeffler. 2021-03-26. Gross--Prasad periods for reducible representations. https://doi.org/10.1515/forum-2021-0089

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