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 certain 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.

中文翻译：

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一些真实表示的 R 群和 WHITTAKER 空间

对于覆盖群的单一无分支真正主级数表示，我们研究相关的R群。对于这种主级数表示的不可约成分，我们证明了一个将R组与惠特克空间维数联系起来的公式。此外，对于半单单连通群的某些饱和覆盖，我们还针对此类维度提出了一个更简单的猜想公式。后一个猜想公式在几个案例中得到验证，包括辛群的覆盖。