Decomposable Specht modules for the Iwahori-Hecke algebra ${\mathcal{H}}_{\mathbb{F},-1}({\mathfrak{S}}_n)$

Abstract

Let $S_{\lambda }$ denote the Specht module defined by Dipper and James for the Iwahori-Hecke algebra ${\mathcal{H}}_n$ of the symmetric group ${\mathfrak{S}}_n$. 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 $\mathcal{H}$ 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 $S_{\lambda }$.

32 pages; minor typos corrected in final version

References in corpus (4)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Blocks of cyclotomic Hecke algebras
• Graded Specht modules
• Universal Specht modules for cyclotomic Hecke algebras

Cited by in corpus (4)

• Generalised column removal for graded homomorphisms between Specht modules
• Specht modules labelled by hook bipartitions I
• Decomposable Specht modules indexed by bihooks
• Decomposable Specht modules indexed by bihooks II