Archimedean zeta integrals for the exterior square L-functions on GLn

Bump and Friedberg introduced a zeta integral interpolating the standard and the exterior square L-functions on GLn simultaneously. We compute the (real) archimedean part of this zeta integral by using the explicit formulas of the principal series Whittaker functions on GLn(R) obtained by Oda and the author. We show that the archimedean zeta integral coincides with the product of two archimedean L-factors.