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

Mixed Schur-Weyl duality between general linear Lie algebras and cyclotomic walled Brauer algebras