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

2014/01/04 by Feinberg, Gabriel, Lee, Kyu-Hwan
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/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.

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