MIT Lie Groups Seminar

Wednesday, March 04, 2020 at 4:30pm to 5:30pm

Room : 2 - 142 182 memorial Drive, Cambridge, MA 02142

Featured SpeakerGeorge Lusztig (MIT Mathematics)

Title :   On induction of class functions.

Abstract :  Let G be a reductive connected group over $Fq$ and let $L$ be a Levi subgroup defined over $Fq$ of a parabolic $P$ of $G$. Then one has the cohomological induction map $RG$ from class functions on $L(Fq)$ to class functions on $G(Fq)$. When $L$ is a $L,P torus,$ this map appeared in my 1976 paper with Deligne and is independent of $P$. In the general case it is also known to be independent of $P$ but only if we assume that $q$ is large. We now define in a different way a map from class functions on $L(Fq)$ to class functions on $G(Fq)$ which does not depend on $P$ and which coincides with the previous map when $q$ is large.

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