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

Kei Yuen Chan Fudan University

Representation Theory mathscidoc:2105.30001

Inventiones mathematicae, 2021.2
Let F be a non-Archimedean local field. This paper studies homological properties of irreducible smooth representations restricted from GLn+1(F) to GLn(F). A main result shows that each Bernstein component of an irreducible smooth representation of GLn+1(F) restricted to GLn(F) is indecomposable. We also classify all irreducible representations which are projective when restricting from GLn+1(F) to GLn(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.
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  title={Homological branching law for (GL𝑛+1(𝐹),GL𝑛(𝐹)): projectivity and indecomposability},
  author={Kei Yuen Chan},
  booktitle={Inventiones mathematicae},
Kei Yuen Chan. Homological branching law for (GL𝑛+1(𝐹),GL𝑛(𝐹)): projectivity and indecomposability. 2021. In Inventiones mathematicae. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210512105114838427820.
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