Algebra Seminar: Mathas -- Content systems and KLR algebras

Andrew Mathas (University of Sydney) 

Friday 8 April, 12-1pm, Place: Carslaw 273 

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.