


Speaker: Prashant Arote, IISER Pune.
Title: HarishChandra Induction and Jordan Decomposition of Characters
Abstract:
Let G be a connected reductive group defined over a finite field 𝔽q and let
F:G→ G be the corresponding Frobenius morphism.
Let L be a Levi factor of a Fstable parabolic subgroup of G.
Endomorphism algebras of representations parabolically induced from cuspidal representations
of LF were described by Howlett and Lehrer.
In this talk, we show that any such algebra is isomorphic to the twisted endomorphism algebra
of a representation which is parabolically induced from a unipotent cuspidal representation of
Levi subgroup of a finite reductive group.
As an application, we show that for any finite connected reductive group, a Jordan decomposition
can be chosen such that it commutes with HarishChandra induction.
This is a joint work with Manish Mishra.
We will have *Sridhar Narayanan* speaking in our RTAG seminar from 2pm to 3:30pm on Friday. Here are the necessary details for his 4th talk: Time: Friday, 26 August, 2:00 – 3:30 pm. Venue : Room No 215, Department of mathematics. Title: OkounkovVershik approach to the representation theory of symmetric groups. Abstract: In this series of talks we will bootstrap the representation theory of symmetric groups inductively, following the 2005 revision of Vershik's and Okounkov's seminal paper on the topic. We have now a dedicated website where one can find the notes and resources from the past meets and announcements of the upcoming meetings: https://sites.google.com/view/rtag/
Speaker: Suprajo das, IIT Bombay Date and time: 26 August 2022, 3.30pm5.00 pm Venue: Ramanujan Hall Title: Numerical aspects of Epsilon multiplicity III Abstract: In the third talk on this topic we shall focus on the epsilon multiplicity of ideals in a regular local ring of dimension 3. We will mostly give a survey of the known results and discuss some open questions in this setup.