On linear periods

2013/07/29 by Zhang, Chong · 2 citations
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1307.7570

Abstract

Let π' be a cuspidal automorphic representation of GL_2n, which is assumed to be the Jacquet-Langlands transfer from a cuspidal automorphic representation π of GL_2m(D), where D is a division algebra so that GL_2m(D) is an inner form of GL_2n. In this paper, we consider the relation between linear periods on π and π'. We conjecture that the non-vanishing of the linear period on π would imply the non-vanishing of that on π'. We illustrate an approach using a relative trace formula towards this conjecture, and prove the existence of smooth transfer over non-archimedean local fields.

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