On the local Bump-Friedberg L function II

2014/11/21 by Matringe, Nadir
#11F66 #11F70 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1411.6046

Abstract

Let F be a p-adic field with residue field of cardinality q. To each irreducible representation of GL(n,F), we attach a local Euler factor L^BF(q^-s,q^-t,π) via the Rankin-Selberg method, and show that it is equal to the expected factor L(s+t+1/2,ϕ_π)L(2s,Λ²∘ ϕ_π) of the Langlands' parameter ϕ_π of π. The corresponding local integrals were introduced in [BF], and studied in [M15]. This work is in fact the continuation of [M15]. The result is a consequence of the fact that if δ is a discrete series representation of GL(2m,F), and χ is a character of Levi subgoup L=GL(m,F)× GL(m,F), trivial on GL(m,F) embedded diagonally, then δ is (L,χ)-distinguished if an only if it admits a Shalika model, a result which was only established for χ=1 before.

Related

• On the local Bump-Friedberg L-function
• Interpolating local constants in families
• On the dependence of the local Rankin-Selberg gamma factors of \textrmSp_2n× \textrmGL_m on ψ
• On the Rankin-Selberg L-factors for \rm SO₅×\rm GL₂
• The local Langlands correspondence for GL(n) over p-adic fields