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Group, Lie and Number Theory Seminar

The explicit Zelevinsky-Aubert involution
Monday, September 19, 2022
4:30-5:30 PM
4088 East Hall Map
Let F be a local non-archimedian field. In 1980, A. Zelevinsky defined an involution pi -> pi^t in the Grothendieck group of finite length complex smooth representations of GL(n,F) and conjectured that this involution preserves irreducibility. A.-M. Aubert showed that Zelevinsky's definition can be extended to the Grothendieck group of finite length complex smooth representations of any connected reductive p-adic group G and proved that the involution preserves irreducibility. In 1986, C. Moeglin et J.-L. Waldspurger gave an algorithm to compute the Langlands parameters of pi^t in terms of the parameters of pi in the case where pi is an irreducible representation of GL(n,F). In this talk I will treat the case where G is the group Sp(2n,F) or SO(2n+1,F). It is a joint work with H. Atobe. Speaker(s): Alberto Minguez (University of Vienna)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics