Geodesic
Homogeneous Representations of Type A KLR-Algebras and Dyck Paths
Séminaire lotharingien de combinatoire, Tome 75 (2016-2019)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

The Khovanov-Lauda-Rouquier (KLR) algebra arose out of attempts to categorify quantum groups. Kleshchev and Ram proved a result reducing the representation theory of these algebras of finite type to the study of irreducible cuspidal representations. In type A, these cuspidal representations are included in the class of homogeneous representations, which are related to fully commutative elements of the corresponding Coxeter groups. In this paper, we study fully commutative elements using combinatorics of Dyck paths. Thereby we classify and enumerate the homogeneous representations for KLR algebras of types A and obtain a dimension formula for some of these representations from combinatorics of Dyck paths. 

@article{SLC_2016-2019_75_a1,
     author = {Gabriel Feinberg and Kyu-Hwan Lee},
     title = {Homogeneous {Representations} of {Type} {A} {KLR-Algebras} and {Dyck} {Paths}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {75},
     year = {2016-2019},
     url = {http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a1/}
}
TY  - JOUR
AU  - Gabriel Feinberg
AU  - Kyu-Hwan Lee
TI  - Homogeneous Representations of Type A KLR-Algebras and Dyck Paths
JO  - Séminaire lotharingien de combinatoire
PY  - 2016-2019
VL  - 75
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a1/
ID  - SLC_2016-2019_75_a1
ER  - 
%0 Journal Article
%A Gabriel Feinberg
%A Kyu-Hwan Lee
%T Homogeneous Representations of Type A KLR-Algebras and Dyck Paths
%J Séminaire lotharingien de combinatoire
%D 2016-2019
%V 75
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a1/
%F SLC_2016-2019_75_a1
Gabriel Feinberg; Kyu-Hwan Lee. Homogeneous Representations of Type A KLR-Algebras and Dyck Paths. Séminaire lotharingien de combinatoire, Tome 75 (2016-2019). http://geodesic.mathdoc.fr/item/SLC_2016-2019_75_a1/