  It is known that the semi-infinite cohomology spaces of the infinitely
twisted nilpotent subalgebra in an affine Lie algebra $g$ with coefficients in
an integrable simple module over the affine Lie algebra have a base enumerated
by elements of the corresponding affine Weyl group graded by the semiinfinite
length function. Let $U$ be the affine quantum group corresponding to $g$. It
is possible to define a subalgebra in $U$ being the quantum analogue of the
universal enveloping algebra of the infinitely twisted nilpotent subalgebra in
$g$. In this paper we prove that for general values of the parameter $v$ the
semiinfinite cohomology of this associative algebra with coefficients in an
integrable simple module over $U$ coincides with the one of the corresponding
Lie subalgebra in $g$ with coefficients in the corresponding $g$-module.

Quantum Algebra;Quantum Algebra