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For a unitary unramified genuine principal series representation of acovering group, we study the associated R-group. We prove a formula relatingthe R-group to the dimension of the Whittaker space for the irreducibleconstituents of such a principal series representation. Moreover, for saturatedcovers of a semisimple simply-connected group, we also propose a simplerconjectural formula for such dimensions. This latter conjectural formula isverified in several cases, including covers of the symplectic groups.

R-group and Whittaker space of some genuine representations