It is well known that n-dimensional projective group gives rise to a
non-homogenous representation of the Lie algebra sl(n+1) on the polynomial
functions of the projective space. Using Shen's mixed product for Witt algebras
(also known as Larsson functor), we generalize the above representation of
sl(n+1) to a non-homogenous representation on the tensor space of any
finite-dimensional irreducible gl(n)-module with the polynomial space.
Moreover, the structure of such a representation is completely determined by
employing projection operator techniques and well-known Kostant's
characteristic identities for certain matrices with entries in the universal
enveloping algebra. In particular, we obtain a new one parameter family of
infinite-dimensional irreducible sl(n+1)-modules, which are in general not
highest-weight type, for any given finite-dimensional irreducible
sl(n)-module. The results could also be used to study the quantum field
theory with the projective group as the symmetry.Comment: 24page
