  In this paper, an explicit expression for the Casimir operator (or the
Casimir invariant) of the inhomogeneous group ISL(n,R) in its enveloping
algebra is proposed, which using contractions of the tenso- rial indices of the
generating operators P^{rho} and E^{nu}{mu} may be presented in the following
(slightly more comprehensible as equation (1)) form. The Casimir is obtained by
symmetrizing this expression. This tensor form is useful in the classification
of particles in affine gravitational gauge theories; such as that based on
ISL(4,R). It is also proven that the Casimir of ISL(n,R) can be decomposed in
terms of the Casimirs of its little groups, a key point in the posterior
construction of its irreducible representations.
