Finite-Sum Realization of Archimedean Asai and Exterior-Square $L$-Factors

We prove that the archimedean Asai $L$-factor attached to an irreducible generic representation of ${\mathrm{GL}}_n(\mathbb{C})$ can be expressed as a finite sum of Flicker local zeta integrals. For an archimedean local field $F$, we also prove that the exterior-square $L$-factor attached to an irreducible generic representation of ${\mathrm{GL}}_m(F)$ can be expressed as a finite sum of Jacquet–Shalika local zeta integrals.