Finite Dimensional Representations of Khovanov-Lauda-Rouquier algebras I: Finite Type

By Peter J. McNamara. 2012

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We classify simple representations of Khovanov-Lauda-Rouquier algebras in finite type. The classification is in terms of a standard family of representations that is shown to yield the dual PBW basis in the Grothendieck group. Finally, we prove a conjecture describing the global dimension of these algebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1abf88d384902a35d774d0689481547a9bd4e9b1