Equivalent definitions of Arthur packets for real classical groups

Adams, Jeffrey; Robert, Nicolás Arancibia; Mezo, Paul

doi:10.48550/arxiv.2108.05788

Cited by 1 publication

(29 citation statements)

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“…The next result follows from [AdC], [ABV] and [AV,Theorem 3.11]. Our proof follows that of [AAM,Lemma 2.2].…”

Section: Extended Groups For Unitary Groups and The Complex General L...supporting

confidence: 59%

“…or equivalently, with ∨ R C/R GL N -orbits of quasiadmissible homomorphisms. The definition of the latter bijection is almost identical to the one in [AAM,Lemma 2.2] and is left to the reader.…”

Section: Extended Groups For Unitary Groups and The Complex General L...mentioning

confidence: 99%

“…The restriction of such a distribution character to the non-identity component GL N (C) ⋊ ϑ (when non-zero) is what we we mean by an irreducible twisted character of GL N (C) (cf. [AAM,(42)]) . We define…”

Section: Grothendieck Groups Of Characters and Twisted Charactersmentioning

confidence: 99%

“…The definitions depend on a pairing between characters and sheaves. We also define a pairing between twisted characters and twisted sheaves for R C/R GL N ([CM, Sections 5-6], [AAM,Section 3]). The key properties of this twisted pairing are listed in this section and shall be proved in Section 4.…”

Section: Sheaves Pairings and Characteristic Cyclesmentioning

confidence: 99%

“…for ϑ-fixed complete geometric parameters ξ. Once sheaves are aligned with characters in this manner, the rest of the proof of (20) follows [ABV] and [AAM,Section 4].…”

Section: Introductionmentioning

confidence: 99%

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Equivalent definitions of Arthur packets for real quasisplit unitary groups

Robert¹,

Mezo²

2022

Preprint

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Mok has defined Arthur packets for quasisplit unitary groups. His definition follows Arthur's work on classical groups and relies on harmonic analysis. For real groups there is an alternative definition of Arthur packets, due to Adams-Barbasch-Vogan. It relies on sheaf-theoretic techniques instead of harmonic analysis. We prove that these two definitions of Arthur packets are equivalent in the case of real quasisplit unitary groups.

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“…The next result follows from [AdC], [ABV] and [AV,Theorem 3.11]. Our proof follows that of [AAM,Lemma 2.2].…”

Section: Extended Groups For Unitary Groups and The Complex General L...supporting

confidence: 59%

Section: Extended Groups For Unitary Groups and The Complex General L...mentioning

confidence: 99%

Section: Grothendieck Groups Of Characters and Twisted Charactersmentioning

confidence: 99%

Section: Sheaves Pairings and Characteristic Cyclesmentioning

confidence: 99%

“…for ϑ-fixed complete geometric parameters ξ. Once sheaves are aligned with characters in this manner, the rest of the proof of (20) follows [ABV] and [AAM,Section 4].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations