Izvorni znanstveni članak

https://doi.org/10.21857/ydkx2cv259

On the non-vanishing of Shalika newvectors at the identity

Harald Grobner ; Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria
Nadir Matringe ; IMJ-PRG, Université Paris-Cité, 8 Pl. Aurélie Nemours, 75013 Paris, France

Sažetak

Let π be an irreducible admissible unitary ψ-generic representation of the non-archimedean general linear group GL2n(F), which admits an (η, psi;)-Shalika model Sψη(π). In this paper, we show the nonvanishing of all non-zero Shalika newvectors So ∈ Sψη(π) at the identity matrix g = id ∈ GL2n(F), if η is unramified. This complements the analogous result for Whittaker newvectors, which can be read off the formulae established independently by Miyauchi in [Miy14] and the second named author in [Mat13].

Ključne riječi

Shalika models; Whittaker models; non-vanishing; local fields

Hrčak ID:

313626

URI

https://hrcak.srce.hr/313626

Datum izdavanja:

24.1.2024.

Posjeta: 572 *