2023/02/07 by Dipendra Prasad, Prasad, Dipendra · 1 citation
Mathematics · #11F70 #22E55 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2302.03492
openalex publication_date 2023/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this mostly expository article, we consider certain homological aspects of branching laws for representations of a group restricted to its subgroups in the context of p-adic groups. We follow our earlier paper, ICM 2018 proceedings, updating it with some more recent works. In particular, following Chan and Chan-Savin, see many of their papers listed in the bibliography, we have emphasized in this work that the restriction of a (generic) representation π of a group G to a closed subgroup H (most of the paper is written in the context of GGP) turns out to be a projective representation on most Bernstein blocks of the category of smooth representations of H. Further, once π|H is a projective module in a particular Bernstein block, it has a simple structure.