OIST Representation Theory Seminar

Andrew Mathas, University of Sydney

Title: Content systems and KLR algebras

Abstract: In 1901 Young gave an explicit construction of the ordinary irreducible representations of the symmetric groups. In doing this, he introduced content functions for partitions, which are now a key statistic in the semisimple representation theory of the symmetric groups. In this talk I will describe a generalisation of Young's ideas to the cyclotomic KLR algebras of affine types A and C. This is quite surprising because Young's seminormal forms are creatures from the semisimple world whereas the cyclotomic KLR algebras are rarely semisimple. As an application, we show that these algebras are cellular and construct their irreducible representations. A special case of these results gives new information about the symmetric groups in characteristic p>0. If time permits, I will describe how these results lead to an explicit categorification of the corresponding integrable highest weight modules. This is joint work with Anton Evseev.