Representations of the Group of Upper Triangular Matrices

Abstract

Let B(n, IR) be the group of real upper triangular matrices of order n with unity on the main diagonal. The subgroup of matrices which have zeros in the last column above the main diagonal is isomorphic to the group B(n-1, R). This allows to define the imbedding of the groups: $$ B(n - 1,\mathbb{R}) \backepsilon g \mapsto \left[ {\begin{array}{*{20}{c}} g&0 0&1 \end{array}} \right] \in B(n,\mathbb{R}). $$