Irreducible representations of Khovanov-Lauda-Rouquier algebras

The representation theory of KLR algebras categorifies quantum groups. In particular there is one simple (finite dimensional) KLR module for each node in the crystal graph B(\infty), and one can use crystal operators to construct them by taking a simple quotient of a particular induced module. In finite type there are several ways to do this, including the adapted string construction of Benkart-Kang-Oh-Park, as well as work of Kleshchev-Ram and McNamara. I'll discuss some of these results and related ideas.

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