Gross--Prasad periods for reducible representations

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.

Revised version, to appear in Forum Mathematicum

References in corpus (2)

• On local zeta-integrals for GSp(4) and GSp(4) x GL(2)
• On p-adic regulators for GSp(4) x GL(2) and GSp(4) x GL(2) x GL(2)

Cited by in corpus (4)

• Ext-Multiplicity Theorem for Standard Representations of $({\mathrm{GL}}_{n+1},{\mathrm{GL}}_n)$
• On integral aspects of Asai periods and Euler systems for ${\mathrm{Res}}_{E/\mathbf{Q}}{\mathrm{GL}}_2$
• A universal Euler system for GSp(4)
• Higher Ext-groups and Relatively Supercuspidal Spectra