The Segre embedding of the quantum conformal superspace

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).

The q-linked complex Minkowski space, its real forms and deformed isometry groups

“…. Technically this is realized, along the line of [17,18,19,20,21] (see also [22,23,24] for a generalization to the super setting) and [25,26]. We also speculate on the interpretation of the "new" parameter ℓ , showing that the product of two ℓ commuting (or linked) quantum planes (or quantum spinors in the physical language [27]) reproduces the deformed algebra of the complex q-linked Minkowski space.…”

Quantum Chiral Superfields

“…This paper is a summary of results obtained in a series of papers by the authors, see for example [3,4,5,6].…”

“…The difference is significant: For the quantum superflag the commutation relations among the generators are much more difficult to compute, since they describe the two dual Grassmannians Gr(2|0, 4|1) and Gr(2|1, 4|1) and, moreover, one would have to compute the quantum twistor relations. In fact, the problem of quantizing the flag supermanifold Fl(2|0, 2|1, 4|1) was approached in [5] with a less direct formalism, in terms of a quantum section.…”

$N=2$ quantum chiral superfields and quantum super bundles

“…The condition of invertibility of the determinant function a 11 a 22 − a 12 a 21 accounts for the condition in (6).…”

“…The superflag F l(2|0, 2|1, 4|1) can be embedded in the product F l(2|0, 2|1, 4|1) ⊂ Gr(2|0, 4|1) × Gr(2|1, 4|1) , and using the super Segre embedding [6] the superflag is embedded into the projective superspace P 80|64 [7,8].…”