The $Cos^\lambda$ transform on real Grassmann manifolds was first studied in convex geometry. The definition of this integral 
 transform has been later extended to Grassmann manifolds over $\mathbb K$, where $\mathbb K$ denotes the reals, the complex 
 numbers or the quaternions. In this talk we show that the $Cos^\lambda$ transform can be obtained by means of standard intert-
 wining operators between certain generalized principal series representations of $SL(n+1,\mathbb K)$. Representation theoretical 
 methods can therefore be employed in its study. Some of the results are outlined. This is joint work with Gestur Olafsson.