  The construction of a generic representation of $g\ell(n+1)$ or of the
trigonomentric deformation of its enveloping algebra known as algebraic
induction is conveniently formulated in term of Lax matrices. The Lax matrix of
the constructed representation factorises into parts determined by the Lax
matrix of a generic representation of the algebra with reduced rank and others
appearing in the factorised expression of the Lax matrix of the special
Jordan-Schwinger representation.
