Doeke Buursma (University of Oregon, Eugene), Standard modules for KLR algebras of (finite) type A

Abstract:

KLR algebras provide a categorification for the positive part of the quantized universal enveloping algebra of (complex, finite-dimensional, semisimple) lie algebras, in which standard modules play a key role. We discuss standard module theory for KLR algebras, giving an explicit construction of standard modules and their projective resolutions in type A. We describe the extension algebra of the direct sum of the standard modules in some special cases.