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In this paper, a notion of cyclotomic (or level k) walled Brauer algebras a"not sign (k, r, t) is introduced for arbitrary positive integer k. It is proven that a"not sign (k, r, t) is free over a commutative ring with rank k (r + t) (r + t) ! if and only if it is admissible. Using super Schur-Weyl duality between general linear Lie superalgebras and a"not sign (2, r, t) , we give a classification of highest weight vectors of -modules M (pq) (rt) , the tensor products of Kac-modules with mixed tensor products of the natural module and its dual. This enables us to establish an explicit relationship between -Kac-modules and right cell (or standard) a"not sign (2, r, t) -modules over C. Further, we find an explicit relationship between indecomposable tilting -modules appearing in M (pq) (rt) , and principal indecomposable right a"not sign (2, r, t) -modules via the notion of Kleshchev bipartitions. As an application, decomposition numbers of a"not sign (2, r, t) arising from super Schur-Weyl duality are determined.

HIGHEST WEIGHT VECTORS OF MIXED TENSOR PRODUCTS OF GENERAL LINEAR LIE SUPERALGEBRAS