Conjectures and results about parabolic induction of representations of GLn(F)

• 成果类型: Article
• 署名作者: Lapid, Erez; Minguez, Alberto
• 署名单位: Weizmann Institute of Science; University of Vienna
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00982-7
• 发表日期: 2020
• 页码: 695-747
• 关键词: general linear group; irreducible representations; adic groups; Duality

摘要

In 1980 Zelevinsky introduced certain commuting varieties whose irreducible components classify complex, irreducible representations of the general linear group over a non-archimedean local field with a given supercuspidal support. We formulate geometric conditions for certain triples of such components and conjecture that these conditions are related to irreducibility of parabolic induction. The conditions are in the spirit of the Geiss-Leclerc-Schroer condition that occurs in the conjectural characterization of square-irreducible representations. We verify some special cases of the new conjecture and check that the geometric and representation-theoretic conditions are compatible in various ways.