Discriminants Of The Specht Modules For Degenerate Cyclotomic Hecke Algebras

Assume that F is a field and either charF=0 or charF large enough. In this paper, we will prove Jantzen sum formulae for the degenerate cyclotomic q-Schur algebra SF and degenerate cyclotomic Hecke algebra HF over field F. Use this formula, we give a criterion for discriminants of SF and HF being non-degenerate and classify the blocks of irreducible modules of Sf and HF.Let F be a field with charF=p>0. We will prove the category of HF-modules and the category of modules of group algebras of some symmetric groups are Morita equivalent under certain conditions. Use this consequence, we can decide whether the discriminants of the cell module of HF contain the factor p or not.In summary, we give a criterion for discriminants of degenerate cyclotomic Hecke algebra HF being non-degenerate over an arbitrary field, this is the main result of the paper.