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gamma factor

Journal of the Institute of Mathematics of Jussieu (1)

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R-GROUP AND WHITTAKER SPACE OF SOME GENUINE REPRESENTATIONS
Part of
- Discontinuous groups and automorphic forms
- Lie groups
Fan Gao
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 1 / January 2023

Published online by Cambridge University Press:

08 March 2021, pp. 213-273

Print publication:

January 2023
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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.