Quantized mixed tensor space and Schur – Weyl duality
نویسندگان
چکیده
Generically (for r + s ≥ n) the centralizer algebra for the action of GLn(C) on mixed tensor space (C n) ⊗r ⊗ ((C n) *) ⊗s is a certain subalgebra of the Brauer algebra, known as the walled (or rational) Brauer algebra. This paper studies a q-deformation, B n r,s (q), of the walled Brauer algebra and shows that the centralizer algebra for the action of the quantum group UR(gl n) on mixed tensor space (R n) ⊗r ⊗ ((R n) *) ⊗s is generated by the action of B n r,s (q). Here R is a commutative ring and UR(gl n) is a specialization of the generic quantum group Uq(gl n) at R. The result holds for any r, s ,n and any specialization of the quantum parameter q (including roots of unity).
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