Journal of Combinatorics

Volume 6 (2015)

Number 4

Fully commutative elements of type $D$ and homogeneous representations of KLR-algebras

Pages: 535 – 557



Gabriel Feinberg (Department of Mathematics and Statistics, Haverford College, Haverford, Pennsylvania, U.S.A.)

Kyu-Hwan Lee (Department of Mathematics, University of Connecticut, Storrs, Conn., U.S.A.)


In this paper, we decompose the set of fully commutative elements into natural subsets when the Coxeter group is of type $D_n$, and study combinatorics of these subsets, revealing hidden structures. (We do not consider type $A_n$ first, since a similar decomposition for type $A_n$ is trivial.) As an application, we classify and enumerate the homogeneous representations of the Khovanov–Lauda–Rouquier algebras of type $D_n$.


fully commutative elements, KLR algebra, homogeneous representation

2010 Mathematics Subject Classification

Primary 16G99. Secondary 05E10.

Published 31 July 2015