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R-GROUP AND WHITTAKER SPACE OF SOME GENUINE REPRESENTATIONS

Part of: Lie groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  08 March 2021

Fan Gao Open the ORCID record for Fan Gao [Opens in a new window]
Fan Gao*
Affiliation:
School of Mathematical Sciences, Yuquan Campus, Zhejiang University, 38 Zheda Road, Hangzhou, China 310027 (gaofan@zju.edu.cn)
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Abstract

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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.

Keywords

covering groupsR-groupsWhittaker functionalsscattering matrixgamma factorPlancherel measure

MSC classification

Primary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 1 , January 2023 , pp. 213 - 273
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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