Advances in Theoretical and Mathematical Physics

Volume 22 (2018)

Number 8

The Segre embedding of the quantum conformal superspace

Pages: 1939 – 2000

DOI: https://dx.doi.org/10.4310/ATMP.2018.v22.n8.a4

Authors

R. Fioresi (Dipartimento di Matematica, Università di Bologna, Italy)

E. Latini (Dipartimento di Matematica, Università di Bologna, Italy; and INFN, Sezione di Bologna, Italy)

M. A. Lledó (Departament de Física, Teòricam Universitat de València; and IFIC (CSIC-UVEG), Burjassot (València), Spain)

F. A. Nadal (Departament de Física Teòricam Universitat de València; and IFIC (CSIC-UVEG), Burjassot (València), Spain)

Abstract

In this paper we study the quantum deformation of the superflag $\mathrm{Fl}(2 \vert 0, 2 \vert 1, 4 \vert 1)$, 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 $\mathrm{SL}_q (4 \vert 1)$.

Published 15 July 2019