University of Sydney Algebra Seminar

Peter Tingley (Loyola University of Chicago)

Friday 24 February, 12-1pm, Place: Carslaw 454

PBW bases and KLR algebras.

Lusztig’s canonical basis is a fairly miraculous object that, among other things, gives a chosen basis for every finite dimensional irreducible representation of a simple Lie algebra over C. Lusztig’s earliest construction made use of his PBW bases, which are less canonical bases of the same space. KLR algebras, which are much more recent, give a very natural way to understand this same canonical basis (in type ADE). Unsurprisingly, there is a close connection between these two approaches. I will discuss this connection, along with various implications. This includes joint work with Ben Webster and with Peter J. McNamara.