The Zelevinsky classification of unramified representations of the metaplectic group

详细信息    查看全文

• 作者：Igor Ciganović^a ; ^{igor.ciganovic@math.hr" class="auth_mail" title="E-mail the corresponding author} ; Neven Grbac^b ; ^{neven.grbac@math.uniri.hr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 22D12 ; secondary ; 22E50 ; 22D30 ; 11F85
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：454
• 期：Complete
• 页码：357-399
• 全文大小：716 K

文摘

In this paper a Zelevinsky type classification of genuine unramified irreducible representations of the metaplectic group over a p  -adic field with p≠2$p\ne 2$ is obtained. The classification consists of three steps. Firstly, it is proved that every genuine irreducible unramified representation is a fully parabolically induced representation from unramified characters of general linear groups and a genuine irreducible negative unramified representation of a smaller metaplectic group. Genuine irreducible negative unramified representations are described in terms of parabolic induction from unramified characters of general linear groups and a genuine irreducible strongly negative unramified representation of a smaller metaplectic group. Finally, genuine irreducible strongly negative unramified representations are classified in terms of Jordan blocks. The main technical tool is the theory of Jacquet modules.