A functoriality principle for blocks of \(p\)-adic linear groups. (English) Zbl 1388.22013
Brumley, Farrell (ed.) et al., Around Langlands correspondences. International conference, Université Paris Sud, Orsay, France, June 17–20, 2015. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3573-8/pbk; 978-1-4704-4117-3/ebook). Contemp. Math. 691, 103-131 (2017).
Author’s abstract: Bernstein blocks of complex representations of \(p\)-adic reductive groups have been computed in a large number of examples, in part thanks to the theory of types à la Bushnell and Kutzko. The output of these purely representation-theoretic computations is that many of these blocks are equivalent. In this paper, we promote the idea that most of these coincidences are explained, and many more can be predicted, by a functoriality principle involving dual groups. We prove a precise statement for groups related to \(GL_{n}\), and then state conjectural generalizations in two directions: more general reductive groups and/or integral \(l\)-adic representations.
For the entire collection see [Zbl 1369.11002].
For the entire collection see [Zbl 1369.11002].
Reviewer: L. N. Vaserstein (University Park)
MSC:
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
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