Modular representation theory and hypertoric varieties
Tom Braden (University of Massachusetts, Amherst)
Wednesday 22nd June, 2016 16:30-17:30 Maths 522
One of the earliest successes in geometric representation theory was Springer's construction of the irreducible representations of the symmetric group (or any Weyl group) in the top cohomology of fibers of a resolution of singularities of the nilpotent cone of GL(n). More recently there has been considerable progress extending these ideas to representations and sheaves with positive characteristic coefficients. Life is is more complicated in positive characteristic: the category of representations is no longer semisimple, and this is reflected in the failure of some important geometric tools from characteristic 0 such as the decomposition theorem. In this talk I will describe work with Carl Mautner giving a picture similar to Springer theory where the role of the nilpotent cone is played by hypertoric varieties. We obtain representations of
a new class of algebras which we call "Matroidal Schur algebras", which share many features with their classical cousins.