The Igusa local zeta function of the simple prehomogeneous vector space

GL(1)^4× SL(2n+1), Λ_2oplusΛ_1oplusΛ_1oplusΛ_1

Abstract

We determine an explicit form of the Igusa local zeta function of the simple prehomogeneous vector space (GL(1)^4× SL(2n+1), Λ_2oplusΛ_1oplusΛ_1oplusΛ_1). As for the Igusa local zeta functions and the p-adic Γ-factors of regular reducible simple prehomogeneous vector spaces with universally transitive open orbits, a table for explicit forms is completed by our result together with the result in Hosokawa \cite{h}.