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K-State Today

September 17, 2013

Mathematics Colloquium lecture today

By Reta McDermott

Sponsored by the mathematics department, Alexander Kleshchev, University of Oregon, will present "Representation Theory of Khovanov-Lauda-Rouquier Algebras and Quantum Groups" at 2:30 p.m. today in 122 Cardwell Hall.

Khovanov-Lauda and Rouquier have categorified quantum groups using representation theory of what is now called Khovanov-Lauda-Rouquier, or KLR, algebras. Kleshchev will 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.

Support is provided by the National Science Foundation Graduate Research conference grant DMS-1315268.