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In this paper, we establish Schur–Weyl reciprocity between the quantum general super Lie algebra  and the Iwahori–Hecke algebra . We introduce the sign -permutation representation of  on the tensor space  of  dimensional -graded -vector space . This action commutes with that of  derived from the vector representation on . Those two subalgebras of  satisfy Schur–Weyl reciprocity. As special cases, we obtain the super case (), and the quantum case (). Hence this result includes both the super case and the quantum case, and unifies those two important cases.

Schur–Weyl Reciprocity between the Quantum Superalgebra and the Iwahori–Hecke Algebra