Parabolically induced representations of p-adic G₂ distinguished by SO₄, I

2022/03/11 by Dijols, Sarah
#FOS: Mathematics #Number Theory (math.NT) #Primary 22E50 #Representation Theory (math.RT) #Secondary 20G41

paper · doi:10.48550/arxiv.2203.05713

Abstract

We consider the parabolically induced representations of the symmetric space SO₄\backslash G₂ over a p-adic field using the geometric lemma when the inducing parabolic is P_β. Using an explicit description of the embedding of G₂ in GL₈, we characterize precisely the induced representations which are (SO₄, χ)-distinguished, given a certain type of involutions is chosen.

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