Algebra Seminar: Williamson -- Modular representations, tilting modules and the p-canonical basis

Geordie Williamson (University of Sydney) 

Friday 16 June, 12-1pm, Place: Carslaw 375 

Title: Modular representations, tilting modules and the p-canonical basis.

Abstract: What are the irreducible representations of the symmetric group in
characteristic p? We still don't know very much about this basic question.  I will
describe how Schur-Weyl duality provides a means of translating this question to one
about so-called tilting modules for the general linear group.  Here recent work with
Riche and Achar, Maiksumi, Riche provides a new means of attack via the "p-canonical
basis".  Then a year-long computer calculation led Lusztig and I to a new conjecture,
which I will illustrate with a video.  All the gory details will be discussed in my
course next semester.