Homological branching law for (GLn+1(F), GLn(F)): projectivity and indecomposability

• 成果类型: Article
• 署名作者: Chan, Kei Yuen
• 署名单位: Fudan University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01033-5
• 发表日期: 2021
• 页码: 299-345
• 关键词: general linear group; unitary representations; whittaker models; CLASSIFICATION; series

摘要

Let F be a non-Archimedean local field. This paper studies homological properties of irreducible smooth representations restricted from GL(n+1)( F) to GL(n)( F). A main result shows that each Bernstein component of an irreducible smooth representation of GL(n+1)( F) restricted to GL(n)(F) is indecomposable. We also classify all irreducible representations which are projective when restricting from GL(n+1)( F) to GL(n)( F). A main tool of our study is a notion of left and right derivatives, extending some previous work joint with Gordan Savin. As a by-product, we also determine the branching law in the opposite direction.