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The Zelevinsky classification of unramified representations of the metaplectic


Ciganović, Igor; Grbac, Neven
The Zelevinsky classification of unramified representations of the metaplectic // Journal of algebra, 454 (2016), 357-399 doi:10.1016/j.jalgebra.2015.12.029 (međunarodna recenzija, članak, znanstveni)


Naslov
The Zelevinsky classification of unramified representations of the metaplectic

Autori
Ciganović, Igor ; Grbac, Neven

Izvornik
Journal of algebra (0021-8693) 454 (2016); 357-399

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Metaplectic group, p-adic field, unramified representation, Zelevinsky classification, Jacquet module, negative representation

Sažetak
In this paper a Zelevinsky type classi cation of genuine unrami ed irreducible representations of the metaplectic group over a p-adic eld with p 6= 2 is obtained. The classi cation consists of three steps. Firstly, it is proved that every genuine irreducible unrami ed representation is a fully parabolically induced representation from unrami ed characters of general linear groups and a genuine irreducible negative unrami ed representation of a smaller metaplectic group. Genuine irreducible negative unrami ed representations are described in terms of parabolic induction from unrami ed characters of general linear groups and a genuine irreducible strongly negative unrami ed representation of a smaller metaplectic group. Finally, genuine irreducible strongly negative unrami ed representations are classi ed in terms of Jordan blocks. The main technical tool is the theory of Jacquet modules.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
HRZZ-IP-2013-11-9364 - Automorfne forme, reprezentacije i primjene (Goran Muić, )
University of Rijeka research grant no. 13.14.1.2.02. (Grbac)

Ustanove
Filozofski fakultet, Rijeka,
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


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