|TUESDAY Sep. 17 :|| COLLOQUIUM |
|Title:||Representation Theory of Khovanov-Lauda-Rouquier Algebras and Quantum Groups|
University of Oregon
Abstract: Khovanov-Lauda and Rouquier have categorified quantum groups using representation theory of what is now called Khovanov-Lauda-Rouquier (KLR) algebras. We show how representation theory of KLR algebras allows us to recover PBW and dual PBW bases in quantum groups via theory of standard modules. A prominent role is played by convexity---for quantum groups this was first discovered by Levendorskii and Soibelman. These considerations lead to an important theory of standard modules for KLR algebras, affine cellular structures on these algebras, and an idea of an affine highest weight category. Finiteness of global dimension of KLR algebras also follows, as first established by Kato and McNamara.
|Time and Place:||2:30 PM CW 122|
|Support is provided by NSF Graduate Research conference grant DMS-1315268|