  For a unitary unramified genuine principal series representation of a
covering group, we study the associated R-group. We prove a formula relating
the R-group to the dimension of the Whittaker space for the irreducible
constituents of such a principal series representation. Moreover, for saturated
covers of a semisimple simply-connected group, we also propose a simpler
conjectural formula for such dimensions. This latter conjectural formula is
verified in several cases, including covers of the symplectic groups.
