The Igusa local zeta function of the simple prehomogeneous vector space ${(GL(1)^4\times SL(2n+1),\Lambda_2\oplus\Lambda_1\oplus\Lambda_1\oplus\Lambda_1)}$

Abstract

We determine an explicit form of the Igusa local zeta function of the simple prehomogeneous vector space ( G L ( 1 ) 4 × S L ( 2 n + 1 ) , Λ 2 ⊕ Λ 1 ⊕ Λ 1 ⊕ Λ 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 [2].