Multivariate Riordan groups and their representations

Riordan bases in a power series ring of several variables are introduced as a special type of Schauder bases. As a part of the method of generating differentials, interplay of Riordan bases generalizes Lagrange inversion formulas. The set of Riordan bases has a group law with a specified set of variables as the unit element. Riordan arrays appear in a representation of the group.