  We prove a formula for the dimension of Whittaker functionals of irreducible
constituents of a regular unramified genuine principal series for covering
groups. The formula explicitly relates such dimension to the Kazhdan-Lusztig
representations associated with certain right cells of the Weyl group. We also
state a refined version of the formula, which is proved under some natural
assumption. The refined formula is also verified unconditionally in several
important cases.
