  Motivated by Brundan-Kleshchev's work on higher Schur-Weyl duality, we
establish mixed Schur-Weyl duality between general linear Lie algebras and
cyclotomic walled Brauer algebras in an arbitrary level. Using weakly cellular
bases of cyclotomic walled Brauer algebras, we classify highest weight vectors
of certain mixed tensor modules of general linear Lie algebras. This leads to
an efficient way to compute decomposition matrices of cyclotomic walled Brauer
algebras arising from mixed Schur-Weyl duality, which generalizes early results
on level two walled Brauer algebras.
