Algebra Seminar

Given a p-adic group G, one would like to find a systematic way of constructing all its irreducible representations. As a first approximation, one can parabolically induce irreducible representations of Levi subgroups of G, however, the resulting representations are often reducible. A more refined approach is to consider (analytic) intertwining operators between such induced representations, whose images turn out to be irreducible in many cases. These intertwining operators have proven to be highly useful in a variety of problems, yet their general behavior remains far from fully understood. In the case of general linear groups, conjectures relate their behavior to the geometry of the cotangent bundle of the space of Langlands parameters.

This talk offers a gentle introduction to these topics and reports on recent progress towards these conjectures.

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