Homogeneous representations of Khovanov–Lauda Algebras

  • Arun Ram

    University of Melbourne, Parkville, Australia
  • Alexander S. Kleshchev

    University of Oregon, Eugene, United States


We construct irreducible graded representations of simply laced Khovanov–Lauda algebras which are concentrated in one degree. The underlying combinatorics of skew shapes and standard tableaux corresponding to arbitrary simply laced types has been developed previously by Peterson, Proctor and Stembridge. In particular, the Peterson–Proctor hook formula gives the dimensions of the homogeneous irreducible modules corresponding to straight shapes.

Cite this article

Arun Ram, Alexander S. Kleshchev, Homogeneous representations of Khovanov–Lauda Algebras. J. Eur. Math. Soc. 12 (2010), no. 5, pp. 1293–1306

DOI 10.4171/JEMS/230