An explicit basis for the extended Catalan arrangement of type Dl

Abstract

Motivated by Kawanoue's construction with the finite-sum formulas, we construct an explicit homogeneous basis for the derivation module of the cone of the extended Catalan arrangement of type Dl. We further show that the restriction of this basis at infinity coincides, up to a nonzero constant, with the integral basis constructed by Feigin-Wang-Yoshinaga. This identifies the geometric motivation behind the parameter choices.