  In this paper we study certain homogeneous spaces, which we call generalised
affine Stiefel algebraic varieties. The main aim is to characterise the
canonical divisor of generalised affine Stiefel algebraic varieties in terms of
group representations. Affine Stiefel algebraic varieties and in particular
$S^{n}$ are two special cases of the generalised affine Stiefel algebraic
varieties.
