Affine open covering of the quantized flag manifolds at roots of unity

TL;DR

This paper demonstrates that quantized flag manifolds at roots of unity can be covered by affine open subsets indexed by the Weyl group, revealing their structure as quasi-schemes.

Contribution

It introduces a natural affine open covering of quantized flag manifolds at roots of unity, establishing their quasi-scheme structure.

Findings

Affine open covering parametrized by Weyl group elements

Quantized flag manifold is a quasi-scheme

Provides geometric insight into quantum flag varieties

Abstract

We show that the quantized flag manifold at a root of unity has natural affine open covering parametrized by the elements of the Weyl group. In particular, the quantized flag manifold turns out to be a quasi-scheme in the sense of Rosenberg.