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Remark on representation theory of general linear groups over a non-archimedean local division algebra

Marko Tadić ; Department of Mathematics, University of Zagreb, Bijenièka 30, 10000 Zagreb, Croatia

Puni tekst: engleski, pdf (272 KB) str. 27-53 preuzimanja: 348* citiraj
APA 6th Edition
Tadić, M. (2015). Remark on representation theory of general linear groups over a non-archimedean local division algebra. Rad Hrvatske akademije znanosti i umjetnosti, (523=19), 27-53. Preuzeto s https://hrcak.srce.hr/145095
MLA 8th Edition
Tadić, Marko. "Remark on representation theory of general linear groups over a non-archimedean local division algebra." Rad Hrvatske akademije znanosti i umjetnosti, vol. , br. 523=19, 2015, str. 27-53. https://hrcak.srce.hr/145095. Citirano 29.07.2021.
Chicago 17th Edition
Tadić, Marko. "Remark on representation theory of general linear groups over a non-archimedean local division algebra." Rad Hrvatske akademije znanosti i umjetnosti , br. 523=19 (2015): 27-53. https://hrcak.srce.hr/145095
Harvard
Tadić, M. (2015). 'Remark on representation theory of general linear groups over a non-archimedean local division algebra', Rad Hrvatske akademije znanosti i umjetnosti, (523=19), str. 27-53. Preuzeto s: https://hrcak.srce.hr/145095 (Datum pristupa: 29.07.2021.)
Vancouver
Tadić M. Remark on representation theory of general linear groups over a non-archimedean local division algebra. Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 2015 [pristupljeno 29.07.2021.];(523=19):27-53. Dostupno na: https://hrcak.srce.hr/145095
IEEE
M. Tadić, "Remark on representation theory of general linear groups over a non-archimedean local division algebra", Rad Hrvatske akademije znanosti i umjetnosti, vol., br. 523=19, str. 27-53, 2015. [Online]. Dostupno na: https://hrcak.srce.hr/145095. [Citirano: 29.07.2021.]

Sažetak
In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the irreducible square integrable representations of these groups by segments of cuspidal representations, and a proof of the irreducibility of the tempered parabolic induction. Our proofs are based on Jacquet modules (and the Geometric Lemma, incorporated in the structure of a Hopf algebra). We use only some very basic general facts of the representation theory of reductive p-adic groups (the theory that we use was completed more then three decades ago, mainly in 1970-es). Of the specific results for general linear groups over A, basically we use only a very old result of G. I. Ol’šanskii, which says that there exist complementary series starting from Ind(ρ ⊗ ρ) whenever ρ is a unitary irreducible cuspidal representation. In appendix of [11], there is also a simple local proof of these results, based on a slightly different approach.

Ključne riječi
Non-archimedean local fields; division algebras; general linear groups; Speh representations; parabolically induced representations; reducibility; unitarizability

Projekti
HRZZ / IP / IP-2013-11-9364 / Automorphic forms - Automorfne forme, reprezentacije i primjene

Hrčak ID: 145095

URI
https://hrcak.srce.hr/145095

Posjeta: 495 *