Abstract
Let PJ be the standard parabolic subgroup of SLn associated to a subset J of simple roots, and let be the standard Levi decomposition. We let
and
denote the quantized algebras of regular functions on PJ and LJ, respectively. Following work of the first author, we study the quantum analogue
of an induced coaction and the corresponding subalgebra
of coinvariants. It was previously shown that the smash product algebra
is isomorphic to
In view of this,
– while it is not a Hopf algebra – can be viewed as a quantum analogue of the coordinate ring
In this article we prove that when
is nonzero and not a root of unity,
is isomorphic to a quantum Schubert cell algebra
associated to a certain parabolic element w in the Weyl group of
In this setting, the quantum Schubert cell algebra
is a q-deformation of the universal enveloping algebra of the nilradical of a parabolic subalgebra of
We also compute explicit commutation relations among the Lusztig root vectors for these particular quantized nilradicals and we give explicit algebra isomorphisms from
to
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