Decomposition Numbers Of Cyclotomic BMW And NW Algebras

Motivated by Martin and Cox-De Visschcr’s work (Martin [23], Cox and De Visscher [10]) on the decomposition numbers for Brauer algebras and walled Brauer algebras over the complex field, we give an algorithm to compute the decomposition numbers on the cyclo-tomic Nazarov-Wenzl algebras and cyclotomic Birman-Murakami-Wcnzl algebras over the field κ, with some additional assumptions. Our result show that the multiplicity-free theorem holds for such algebras.