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Kazhdan–Lusztig representations and Whittaker space of some genuine representations

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Abstract

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.

Mathematics Subject Classification

Primary 11F70 Secondary 22E50 20C08 

Notes

Acknowledgements

I would like to thank Caihua Luo for several discussions on the content of Sect. 3. Thanks are also due to the referee for his or her careful reading and insightful comments.

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Authors and Affiliations

  1. 1.School of Mathematical Sciences, Yuquan CampusZhejiang UniversityHangzhouChina

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