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arXiv · 2405.00671

The scalar product formula for parahoric Deligne--Lusztig induction

Charlotte Chan
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Abstract

Parahoric Deligne--Lusztig induction gives rise to positive-depth representations of parahoric subgroups of $p$-adic groups. The most fundamental basic question about parahoric Deligne--Lusztig induction is whether it satisfies the scalar product formula. We resolve this conjecture for all Howe-factorizable split-generic pairs $(T,\theta)$ -- in particular, for all characters $\theta$ when $T$ is elliptic and $p$ is not a torsion prime for the root system of the $p$-adic group.

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Charlotte Chan. 2024-05-01. The scalar product formula for parahoric Deligne--Lusztig induction. https://arxiv.org/abs/2405.00671

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