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Abstract 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 A₍ at the -th root of unity, where is an odd integer satisfying (, n+1) =1 and n+1.
Toshiyuki Tanisaki (Thu,) studied this question.