arXiv:1505.04075 Abstract | arXiv Analytics

arXiv:1505.04075 [math.RT]Abstract References Reviews Resources

Homogeneous representations of Type A KLR-algebras and Dyck paths

Published 2015-05-15Version 1

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 to the study of irreducible cuspidal representations. In the finite 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 type A and obtain a dimension formula for these representations from combinatorics of Dyck paths.

Comments: arXiv admin note: substantial text overlap with arXiv:1401.0845

Categories: math.RT, math.CO

Keywords: dyck paths, homogeneous representations, cuspidal representations, klr-algebras, combinatorics

Related articles: Most relevant | Search more

arXiv:1401.0845 [math.RT] (Published 2014-01-04, updated 2015-07-29)

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

Gabriel Feinberg, Kyu-Hwan Lee

arXiv:2004.08033 [math.RT] (Published 2020-04-17)

Combinatorics of Type D Exceptional Sequences

Emily Carrick, Alexander Garver

arXiv:math/0604333 [math.RT] (Published 2006-04-14)

Combinatorics of $A_2$-crystals