Introduction to Automorphic Forms for $GL(n,\text{BZ})⋉{\text{BZ}}^{(m,n)}$

In this paper, we introduce the notion of automorphic forms for $GL(n,\text{BZ})⋉{\text{BZ}}^{(m,n)}$ and discuss invariant differential operators on the Minkowski-Euclid space. The group $GLn,\text{BR}⋉{\text{BR}}^{(m,n)}$ is the semidirect product of $GL(n,\text{BR})$ and the additive group ${\text{BR}}^{(m,n)}$ and is {\it not} a reductive group. The Minkowski-Euclid space is the quotient space of $GL(n,\text{BR})⋉{\text{BR}}^{(m,n)}$ by $O(n,\text{BR})$. The Minkowski-Euclid space is an important non-symmetric homogeneous space geometrically and number theoretically. We present some open problems to be solved in the future.