Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584646 | Journal of Algebra | 2014 | 38 Pages |
Abstract
Let SλSλ denote the Specht module defined by Dipper and James for the Iwahori–Hecke algebra HnHn of the symmetric group SnSn. When e=2e=2 we determine the decomposability of all Specht modules corresponding to hook partitions (a,1b)(a,1b). We do so by utilising the Brundan–Kleshchev isomorphism between HH 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 SλSλ is indecomposable. When n is odd, we find an endomorphism of SλSλ and use it to obtain a generalised eigenspace decomposition of SλSλ.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Liron Speyer,