Reduction of Quantum Principal Bundles over non affine bases

TL;DR

This paper develops a sheaf-theoretic framework for reducing quantum principal bundles over projective bases, with applications to classical models like projective spaces and specific group reductions.

Contribution

It introduces a sheaf-theoretic approach to quantum bundle reduction and applies it to classical examples such as projective spaces and group subgroup reductions.

Findings

Effective application of sheaf theory to quantum bundle reduction

Characterization of reductions in the sheaf-theoretic setting

Analysis of classical models like the Klein projective space

Abstract

In this paper we develop the theory of reduction of quantum principal bundles over projective bases. We show how the sheaf theoretic approach can be effectively applied to certain relevant examples as the Klein model for the projective spaces; in particular we study in the algebraic setting the reduction of the principal bundle $\mathrm{GL}(n) \to \mathrm{GL}(n)/P= \mathbf{P}^{n-1}(\mathbb{C})$ to the Levi subgroup $G_0$ inside the maximal parabolic subgroup $P$ of $\mathrm{GL}(n)$. We characterize reductions in the sheaf theoretic setting.