A note on the canonical divisor of the generalised affine Stiefel algebraic varieties

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.