The Segre embedding of the quantum conformal superspace

TL;DR

This paper develops a quantum deformation of the superflag and its big cell, using a generalized Segre map to embed them projectively and construct quantum coordinate superrings with symmetry actions.

Contribution

It introduces a novel quantum deformation framework for superflags and their embeddings, extending classical geometric concepts into the quantum super setting.

Findings

Quantum deformation of superflag and big cell constructed

Projective embedding via generalized Segre map realized

Quantum coordinate superring with conformal supergroup coaction

Abstract

In this paper study the quantum deformation of the superflag Fl(2|0, 2|1,4|1), and its big cell, describing the complex conformal and Minkowski superspaces respectively. In particular, we realize their projective embedding via a generalization to the super world of the Segre map and we use it to construct a quantum deformation of the super line bundle realizing this embedding. This strategy allows us to obtain a description of the quantum coordinate superring of the superflag that is then naturally equipped with a coaction of the quantum complex conformal supergroup SL_q(4|1).