Quantized enveloping algebras are quantum analogues of the universal enveloping algebras corresponding to semisimple and reductive Lie algebras over C, and they are used in quantum statistical mechanics, Lie theory and knot theory. q-Schur algebras S_q(n,r) are auantum analogues of the 'classical' Schur algebras S(n,r) that classify the homogeneous polynomial representations of GL_n of degree r over C. The q-Schur algebras S_q(n,r) have applications in the representation theory of GL_n
over the field F_q. U_A(gl_n) is the integral form of the quantized universal eneveloping algebra of the Lie algebra gl_n. The relationship
between U_A(gl_n) and S_q(n,r) are investigated in terms of quantized codeterminants associated with the q-Schur algebras. Corresponding Young diagram representations are also presented in this context.
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