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Modular representations of p-adic groups and the Jacquet—Langlands correspondence
If you have a question about this talk, please contact Christopher Brookes.
The Jacquet—Langlands correspondence is a bijection between certain irreducible complex representations of a general linear group over a p-adic field and an inner form of such a group, defined by a character relation. While the existence of the correspondence has been known since the 1980s, it is not yet known how to make it explicit in general, even though there are classifications of the irreducible representations on both sides (and more); moreover, all results so far (mostly due to Bushnell—Henniart) have concentrated on the ``cuspidal’’ case, where the character relation is more amenable to computation.
As well as trying to explain what these words mean, I will report on work where we bring the mod-l representation theory of p-adic groups to bear on this question (for l a prime different from p), in particular reducing most of the problem to the cuspidal case.
This talk is part of the Algebra and Representation Theory Seminar series.
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