The Koszul complex and a certain induced module for a quantum group

Toshiyuki Tanisaki

Published 2022-12-24Version 1

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 $A_n$ at the $\ell$-th root of unity, where $\ell$ is an odd integer satisfying $\ell\geqq n+1$.