Journal of Combinatorics
Volume 6 (2015)
Fully commutative elements of type $D$ and homogeneous representations of KLR-algebras
Pages: 535 – 557
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.