On coordinate expressions of jet groups and their representations (Q1980315)

Denote by \(L^r_n=J^r_0(\mathbb R^n,\mathbb R^n)_0\) the space of \(r\)-jets of smooth maps from \(\mathbb R^n\) to itself preserving the origin. Then the invertible elements of \(L^r_n\) form a group \(G^r_n\) called the jet group. The present paper deals with the coordinate expression and matrix representations of jet groups \(G^1_2\), \(G^2_1\), \(G^2_2\), \(G^3_1\) and \(G^6_1\). The author also studies Toupin subgroups. For the entire collection see [Zbl 1468.53002].