The ring of differential operators on a quantized flag manifold

TL;DR

This paper investigates the structure of the ring of differential operators on a quantized flag manifold, providing explicit descriptions of its localizations using quantum algebra techniques.

Contribution

It offers a detailed analysis and explicit description of the differential operator ring on quantized flag manifolds, advancing understanding in quantum algebra and geometry.

Findings

Explicit description of the localization of the differential operator ring.

Connection between the differential operators and the quantum Weyl algebra.

Enhanced understanding of the algebraic structure of quantized flag manifolds.

Abstract

We establish some properties of the ring of differential operators on the quantized flag manifold. Especially, we give an explicit description of its localization on an affine open subset in terms of the quantum Weyl algebra ($q$-analogue of boson).