Twisted Kazhdan-Lusztig conjecture for $p$-adic general linear group

Yuan Chai

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arXiv · 2604.21731

Twisted Kazhdan-Lusztig conjecture for $p$-adic general linear group

Yuan Chai

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Abstract

We use enhanced Langlands parameters to obtain a classification for irreducible representations of twisted $p$-adic general linear groups in unramified principal series. We give the definition of standard representations and prove the twisted Kazhdan-Lusztig conjecture for the multiplicities in the Grothendieck group. We mainly follow Lusztig's work in the connected case using graded Hecke algebra. We show that the parametrization is compatible with the Whittaker-normalized one.

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BibTeX RIS

Yuan Chai. 2026-04-23. Twisted Kazhdan-Lusztig conjecture for $p$-adic general linear group. https://arxiv.org/abs/2604.21731

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