Boltje-Maisch resolutions of Specht modules. (Q2437999)

In the representation theory of the symmetric groups, the Specht modules continue to attract a great deal of attention. An important paper of Boltje-Hartmann constructs, in a characteristic-free way, a finite resolution for each Specht module in which the factors are permutation modules; the exactness of this resolution was proved by Santana and Yudin. Boltje and Maisch then considered the analogous problem for Specht modules for the Iwahori-Hecke algebras associated to the symmetric groups; they defined a chain complex which reduces in the case \(q=1\) to the original complex of Boltje-Hartmann. The purpose of the paper under review is to prove the exactness of this complex. The authors mimic a lot of the work of Santana-Yudin, but need to introduce extra tools to deal with the quantum case. The paper is mostly well-written, but suffers from a lack of examples. The authors' English and typesetting would have benefitted from some proper copy-editing.