Seminar

Sylow-trivial representations of a finite group G are kG-modules that split as the trivial module plus a projective module when restricted to a Sylow p-subgroup. One-dimensional modules are obviously such modules, but are there others? My talk will present a quest to classify such modules when G is a finite group of Lie type, by Jon Carlson, Nadia Mazza, Dan Nakano, and myself (whose (hopefully!) final steps are still in progress here at MSRI). The secret ingredients in our work include:  1) A description of such modules in terms of local group theory that I found in recent earlier work 2) The \Phi_d-local theory of finite groups of Lie type of Broue, Malle, Michel, Rouquier.... 3) The collective wisdom about potential such objects gathered from many years of experience and blissful hard work.