Canonical Systems of Basic Invariants for Unitary Reflection Groups

It is known that there exists a canonical system for every finite real reflection group. In a previous paper, the first and the third authors obtained an explicit formula for a canonical system. In this article, we first define canonical systems for the finite unitary reflection groups, and then prove their existence. Our proof does not depend on the classification of unitary reflection groups. Furthermore, we give an explicit formula for a canonical system for every unitary reflection group.