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Under the assumption that the quantum parameter $q$ is an $l$-th primitiveroot of unity with $l$ odd in a field $F$ of characteristic 0 and $m+n\geq r$,we obtained a complete classification of irreducible modules of the $q$-Schursuperalgebra introduced H. Rui and the first Author.

Irreducible representations of q-Schur superalgebras at a root of unity