Symmetric Solutions to Symmetric Partial Difference Equations

Abstract

This paper studies systems of linear difference equations on the lattice ${\mathbb{Z}}^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of symmetries.

Theorem 4.2 in the earlier arxiv version does not charaterise all the symmetric solutions to a symmetric system of difference equations on ${\mathbb{Z}}^n,$ as claimed. Thus, the statement on the dimension of the space of symmetric solutions is an underestimate