| In this paper, we first recall the theory of the symmetric group and associatedIwahori-Hecke algebras. We introduce the minimal length distinguished cosetrepresentatives of Young subgroup in the symmetric group, and investigate differentcombinatorial realization of the distinguished coset representatives. Then we summarize theresults on simple modules over Hecke algebras of type A and related combinatorics. For thetwisted Specht modules constructed via the twisted Murphy basis, we give a labelling ofsimple modules using the Mullineux map. That says, we determine those partitions suchthat the quotients of the corresponding cell modules by the radical of the bilinear forms arenonzero, and we compare this labelling of simple modules with the labelling of simplemodules obtained via the usual Murphy basis. |
