Abstract
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We construct stable geometric and spectral transfer factors for a general reductive
group and develop some of their basic properties, assuming the refined local
Langlands correspondence. Using our definition of stable geometric transfer factors,
we show that the stable transfer conjecture for orbital integrals implies the stable
transfer of characters and vice versa. The latter is also implied by local Langlands,
and in particular this establishes archimedean stable geometric transfer. Finally, we
show how the stable geometric transfer factors can be used to define stable spectral
transfer factors.
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Keywords
stable spectral transfer, stable geometric transfer
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Mathematical Subject Classification
Primary: 22E55
Secondary: 11R39
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Milestones
Received: 29 February 2024
Revised: 16 September 2025
Accepted: 1 November 2025
Published: 10 March 2026
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| © 2026 The Author(s), under
exclusive license to MSP (Mathematical Sciences Publishers).
Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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