University of Sydney Algebra Seminar

Geordie Williamson (University of Sydney)

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

Modular representations, tilting modules and the p-canonical basis

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.