Decomposition numbers of cyclotomic NW and BMW algebras

Motivated by Martin and Cox–De Visscher’s work Martin [18], , Cox and De Visscher [5] on the decomposition matrices for Brauer algebras and walled Brauer algebras over the complex field, we give an algorithm to compute the decomposition matrices on the cyclotomic Nazarov–Wenzl algebras and cyclotomic Birman–Murakami–Wenzl algebras over the field κ with some additional assumptions. Our result shows that the multiplicity-free theorem holds for such algebras.