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We consider the tensor product representation of m copies of the natural representation with n copies of its dual representation for both the general linear group GL(r, C) and the quantum group Uq(gί(r,C)). These tensor spaces determine rational representations of GLr and lfq(g£(r,C)). The centralizer algebras of these representations are, respectively, the complex algebra Brmn^ which is a subalgebra of the Brauer algebra BTm+n, and the algebra H^n(q) over the field of complex rational functions with indeterminate q, which is a generalization of the Iwahori-Hecke algebra. Upon setting q — 1, the algebra H^n(q) specializes to B r mn. The algebra B r

pacific journal of mathematics

Characters of the centralizer algebras of mixed tensor representations ofGL(r,ℂ) and the quantum group 𝒰q(gl(r,ℂ))