Kazhdan-Lusztig representations and Whittaker space of some genuine representations

2019/03/14 by Fan Gao, Gao, Fan
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1903.06069

openalex publication_date 2019/03/14 · openalex created_date 2019/03/22 · openalex updated_date 2026/07/28

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.

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