The Koszul Complex and a Certain Induced Module for a Quantum group

We give a description of a certain induced module for a quantum group of type A. Together with our previous results this gives a proof of Lusztig’s conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra of type Aₙ at the -th root of unity, where is an odd integer satisfying ( ,n+1)=1 and > n+1.