On gamma matrices of local zeta functions associated with homogeneous cones

The purpose of this paper is to investigate coefficient matrices of functional equations of zeta functions associated with homogeneous cones, which are given explicitly in the previous paper, in detail. We prove that the coefficient matrix can be decomposed into variable-wise matrices regardless of the choice of homogeneous cones. Moreover, under a suitable condition, we show that the associated zeta functions admit a kind of completion forms.