Quantized flag manifolds and non-restricted modules over quantum groups at roots of unity

TL;DR

This paper proves Lusztig's conjectural multiplicity formula for non-restricted modules over a specific quantum group at roots of unity, advancing understanding in quantum algebra representation theory.

Contribution

It provides a proof of Lusztig's conjecture for non-restricted modules over De Concini-Kac quantum groups at roots of unity, under certain conditions.

Findings

Proof of Lusztig's multiplicity formula established

Clarifies structure of non-restricted modules at roots of unity

Enhances understanding of quantum group representations

Abstract

We give a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra at the $\ell$-th root of unity, where $\ell$ is an odd prime power satisfying certain reasonable conditions.