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

Gabriel Feinberg; Kyu-Hwan Lee

paper

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

arXiv:1401.0845

Abstract

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 the 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 $D_{n}$ .

arXiv comment19 pages