Types and unitary representations of reductive p-adic groups

• 成果类型: Article
• 署名作者: Ciubotaru, Dan
• 署名单位: University of Oxford
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0790-4
• 发表日期: 2018
• 页码: 237-269
• 关键词: cyclic homology; THEOREM; series

摘要

We prove that for every Bushnell-Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a bijection between irreducible unitary representations in the two categories. Moreover, we show that every irreducible smooth G-representation contains a rigid type. This is a generalization of the unitarity criterion of Barbasch and Moy for representations with Iwahori fixed vectors.