Grading of representations of p-adic groups

Max Gurevich
Technion, Israel Institute of Technology, Haifa

Date(s) : 22/04/2021   iCal
16 h 00 min - 17 h 00 min

The theory of Bernstein blocks and its many later developments allow for a decomposition of a category of smooth complex representations of a p-adic group into categories of modules over concrete finitely-generated algebras. In type A, the Brundan-Kleshchev–Rouquier equivalence says these resulting affine Hecke algebras may be viewed as ungraded analogues of the of (graded) quiver Hecke algebras. Thus, the representation theory of the latter algebras may be viewed as an uncovering of a hidden graded structure on GL_n(p-adic field) representations.
I would like to show the potential of this point of view for tackling natural problems on decomposition of reducible GL_n-representations.
Recently devised tools in works of Kang-Kashiwara-Kim-Oh shed new lights on some subtle properties of the Langlands/Zelevinsky classification and boost our understanding of an alternative classification of irreducible representations using the RSK-correspondence.
This will contain results with Erez Lapid and with Alberto Minguez.



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