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R. Fioresi

Publications and source records attributed to R. Fioresi.

At least 37 records · Page 2Linked to original sources
arXiv2017

The Segre embedding of the quantum conformal superspace

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).

hep-th↗
arXiv2016

A Comparison of the functors of points of Supermanifolds

We study the functor of points and the local functor of points (here called the Weil--Berezin functor) for smooth and holomorphic supermanifolds, providing characterization theorems and fully discussing the representability issues. In the end we examine applications to differential calculus including the transitivity theorems.

math.RA↗
arXiv2016

Representability in Supergeometry

In this paper we use the notion of Grothendieck topology to present a unified way to approach representability in supergeometry, which applies to both the differential and algebraic settings.

math.AG↗
arXiv2016

The Push the button algorithm for contragredient Lie superalgebras

The purpose of the present paper is to explain how the push the button algorithm can be successfully applied to the Vogan superdiagram associated to a contragredient Lie superalgebra, so to obtain the equivalent super version of the Borel-De Siebenthal Theorem.

math.RT↗
arXiv2015

Quantum twistors

We compute explicitly a star product on the Minkowski space whose Poisson bracket is quadratic. This star product corresponds to a deformation of the conformal spacetime, whose big cell is the Minkowski spacetime. The description of Minkowski space is made in the twistor formalism and the quantization follows by substituting the classical conformal group by a quantum group.

hep-th↗
arXiv2015

The Peter-Weyl Theorem for SU(1|1)

We study a generalization of the results \in \cite{cfk} to the case of $SU(1|1)$ interpreted as the supercircle $S^{1|2}$. We describe all of its finite dimensional complex irreducible representations, we give a reducibility result for representations not containing the trivial character, and we compute explicitly the corresponding matrix elements. In the end we give the Peter-Weyl theorem for $S^{1|2}$.

math.RT↗
arXiv2014

SUSY structures, representations and Peter-Weyl theorem for $S^{1|1}$

The real compact supergroup $S^{1|1}$ is analized from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of $({\mathbf C}^{1|1})^\times$ with reduced Lie group $S^1$, and a link with SUSY structures on ${\mathbf C}^{1|1}$ is established. We describe a large family of complex semisimple representations of $S^{1|1}$ and we show that any $S^{1|1}$-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter-Weyl theorem for $S^{1|1}$.

math.RT↗
arXiv2013

On SUSY curves

In this note we give a summary of some elementary results in the theory of super Riemann surfaces (SUSY curves).

math.AG↗
arXiv2012

Super Distributions, Analytic and Algebraic Super Harish-Chandra pairs

The purpose of this paper is to extend the theory of Super Harish-Chandra pairs, originally developed by Koszul for Lie supergroups, to analytic and algebraic supergroups, in order to obtain information also about their representations. We also define the distribution superalgebra for algebraic and analytic supergroups and study its relation with the universal enveloping superalgebra

math.RA↗
arXiv2012

Quadratic deformation of Minkowski space

We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson bracket is quadratic. We show that the star product although defined on the polynomials can be extended differentiably. Finally we compute the Eucliden and Minkowskian real forms of the deformation.

hep-th↗
arXiv2011

Chevalley Supergroups

In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of Chevalley groups, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. In particular both basic (even exceptional) and strange cases are covered. This provides a unified approach to most of the algebraic supergroups considered so far in literature, and an effective method to construct new ones. As an intermediate step, we prove an existence theorem for Chevalley bases of simple classical Lie superalgebras and a PBW-like theorem for their associated Kostant superalgebras.

math.RA↗
arXiv2011

On chiral quantum superspaces

We give a quantum deformation of the chiral Minkowski superspace in 4 dimensions embedded as the big cell into the chiral conformal superspace. Both deformations are realized as quantum homogeneous superspaces: we deform the ring of regular functions together with a coaction of the corresponding quantum supergroup.

hep-th↗
arXiv2010

On the construction of Chevalley Supergroups

We give a description of the construction of Chevalley supergroups, providing some explanatory examples. We avoid the discussion of the $A(1,1)$, $P(3)$ and $Q(n)$ cases, for which our construction holds, but the exposition becomes more complicated. We shall not in general provide complete proofs for our statements, instead we will make an effort to convey the key ideas underlying our construction. A fully detailed account of our work is scheduled to appear later.

math.RA↗
arXiv2010

The quantum chiral Minkowski and conformal superspaces

We give a quantum deformation of the chiral super Minkowski space in four dimensions as the big cell inside a quantum super Grassmannian. The quantization is performed in such way that the actions of the Poincaré and conformal quantum supergroups on the quantum Minkowski and quantum conformal superspaces are presented.

math.QA↗
arXiv2009

The local functors of points of Supermanifolds

We study the local functor of points (which we call the Weil-Berezin functor) for smooth supermanifolds, providing a characterization, representability theorems and applications to differential calculus.

math.RA↗
arXiv2008

Quantization of Projective Homogeneous Spaces and Duality Principle

We introduce a general recipe to construct quantum projective homogeneous spaces, with a particular interest for the examples of the quantum Grassmannians and the quantum generalized flag varieties. Using this construction, we extend the quantum duality principle to quantum projective homogeneous spaces.

math.QA↗
arXiv2008

Quotients in supergeometry

The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.

math.RA↗