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The Zelevinsky classification of unramified representations of the metaplectic (CROSBI ID 245042)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

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

Podaci o odgovornosti

Ciganović, Igor ; Grbac, Neven

engleski

The Zelevinsky classification of unramified representations of the metaplectic

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.

Metaplectic group ; p-adic field ; unramified representation ; Zelevinsky classification ; Jacquet module ; negative representation

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Podaci o izdanju

454

2016.

357-399

objavljeno

0021-8693

1090-266X

10.1016/j.jalgebra.2015.12.029

Povezanost rada

Matematika

Poveznice
Indeksiranost