Gamma factors root numbers and distinction

2016/07/07 by Matringe, Nadir, Offen, Omer
#11F70 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1607.01982

Abstract

We study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of p-adic fields. We show that the local Rankin-Selberg root number of any pair of distinguished representation is trivial and as a corollary we obtain an analogue for the global root number of any pair of distinguished cuspidal representations. We further study the extent to which the gamma factor at 1/2 is trivial for distinguished representations as well as the converse problem.

Related

• Rankin-Selberg gamma factors of level zero representations of GL_n
• On the Rankin-Selberg gamma factor of simple supercuspidal representations of the unitary group for p-adic local fields
• Gamma factors and root numbers of pairs for the Galois and the linear model
• On the dependence of the local Rankin-Selberg gamma factors of \textrmSp_2n× \textrmGL_m on ψ
• Gamma factors for Asai representations of \rm GL₂