Cohomological representations of parahoric subgroups

Chan, Charlotte; Ivanov, Alexander B.

doi:10.48550/arxiv.1903.06153

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Deligne-lusztig Constructions1

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Cited by 2 publications

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“…Recently, this work has been studied and generalised along various aspects; see e.g. [Sta09], [Sta11], [Che18b], [Che20], [CI19]. In this section we study the representations of G(O r ) via Deligne-Lusztig theory in two directions, one through the twisting operators and one through the Springer fibres.…”

Section: Deligne-lusztig Constructionsmentioning

confidence: 99%

Twisting operators and centralisers of Lie type groups over local rings

Chen¹

2020

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We extend the classical result asserting that the twisting operator preserves certain Deligne-Lusztig character values for truncated formal power series; along the way we discuss some properties of centralisers. This leads us to the construction of an action of GL n (F q [[π]]/π r ) on a Springer fibre intersected by Deligne-Lusztig varieties; we determine the primitivities of the induced cohomological representations for single cycles. The case of SL 2 over finite dual numbers is presented with a criterion on semisimple orbit representations.

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Section: Deligne-lusztig Constructionsmentioning

confidence: 99%

Twisting operators and centralisers of Lie type groups over local rings

Chen¹

2020

Preprint

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On loop Deligne--Lusztig varieties of Coxeter-type for inner forms of ${\rm GL}_n$

Chan¹,

Ivanov²

2019

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For a reductive group G over a local non-archimedean field K one can mimic the construction from the classical Deligne-Lusztig theory by using the loop space functor. We study this construction in special the case that G is an inner form of GLn and the loop Deligne-Lusztig variety is of Coxeter type. After simplifying the proof of its representability, our main result is that its -adic cohomology realizes many irreducible supercuspidal representations of G, notably almost all among those whose L-parameter factors through an unramified elliptic maximal torus of G. This gives a purely local, purely geometric and -in a sense -quite explicit way to realize special cases of the local Langlands and Jacquet-Langlands correspondences.

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Cohomological representations of parahoric subgroups

Cited by 2 publications

References 20 publications

Twisting operators and centralisers of Lie type groups over local rings

Twisting operators and centralisers of Lie type groups over local rings

On loop Deligne--Lusztig varieties of Coxeter-type for inner forms of ${\rm GL}_n$

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