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arXiv · 2304.06418

On principal series representations of quasi-split reductive p-adic groups

Maarten Solleveld
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Abstract

Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and its image is an explicitly described set of enhanced L-parameters. Our correspondence is determined by the choice of a Whittaker datum for G, and it is canonical given that choice. We show that our parametrization satisfies many expected properties, among others with respect to the enhanced L-parameters of generic representations, temperedness, cuspidal supports and central characters. Along the way we characterize genericity in terms of representations of an affine Hecke algebra.

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Maarten Solleveld. 2025-01-17. On principal series representations of quasi-split reductive p-adic groups. https://doi.org/10.2140/pjm.2025.334.269

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