Decomposable Specht modules for the Iwahori-Hecke algebra HF,-1(Gn)

JOURNAL OF ALGEBRA

卷:418

Article

Speyer, Liron

关键词: Representation theory;    Symmetric groups;    Hecke algebras;    KLR algebras;    Specht modules;    Decomposable;   

DOI  :  10.1016/j.jalgebra.2014.07.011

来源: Elsevier

【 摘 要 】

Let SA denote the Specht module defined by Dipper and James for the Iwahori-Hecke algebra H-n of the symmetric group G(n). When e = 2 we determine the decomposability of all Specht modules corresponding to hook partitions (a, 1(b)). We do so by utilising the Brundan-Kleshchev isomorphism between H and a Khovanov-Lauda-Rouquier algebra and working with the relevant KLR algebra, using the set-up of Kleshchev-Mathas-Ram. When n is even, we easily arrive at the conclusion that S-lambda is indecomposable. When n is odd, we find an endomorphism of S-lambda and use it to obtain a generalised eigenspace decomposition of S-lambda. (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free