  To a finite dimensional representation of a complex Lie group $G$, an
associative algebra of adjoint covariant polynomial maps from the direct sum of
$m$ copies of the Lie algebra $\mathfrak{g}$ of $G$ into an algebra of complex
matrices is associated. When the tangent representation of the given
representation is irreducible, the center of this algebra of concomitants can
be identified with the algebra of adjoint invariant polynomial functions on
$m$-tuples of elements of $\mathfrak{g}$. For irreducible finite dimensional
representations of $\mathrm{SL}_2(\mathbb{C})$ minimal generating systems of
the corresponding algebras of concomitants are determined, both as an algebra
and as a module over its center.
