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Let  P Jbe the standard parabolic subgroup of  SL nassociated to a subset  J  of simple roots, and letbe the standard Levi decomposition. We letanddenote the quantized algebras of regular functions on  P Jand  L J, respectively. Following work of the first author, we study the quantum analogueof an induced coaction and the corresponding subalgebraof coinvariants. It was previously shown that the smash product algebrais isomorphic toIn view of this,– while it is not a Hopf algebra – can be viewed as a quantum analogue of the coordinate ringIn this article we prove that whenis nonzero and not a root of unity,is isomorphic to a quantum Schubert cell algebraassociated to a certain parabolic element  w  in the Weyl group ofIn this setting, the quantum Schubert cell algebrais a  q -deformation of the universal enveloping algebra of the nilradical of a parabolic subalgebra ofWe also compute explicit commutation relations among the Lusztig root vectors for these particular quantized nilradicals and we give explicit algebra isomorphisms fromto

Quantized nilradicals of parabolic subalgebras of and algebras of coinvariants