R. Quiroga-Barranco

activity

20072024

most citedIsometric actions of simple groups and transverse structures: The integrable normal case

5 citations · 7 across the 28 of their papers we have counts for

collaborators

31 papers

math.CV2024

Geometry of the slice regular Möbius transformations of the quaternionic unit ball

Raul Quiroga-Barranco

For the quaternionic unit ball $B$ , let us denote by $M (B)$ the set of slice regular Möbius transformations mapping $B$ onto itself. We introdu…

math.FA2024

Toeplitz operators and group-moment coordinates for quasi-elliptic and quasi-hyperbolic symbols

Raul Quiroga-Barranco, Armando Sanchez-Nungaray

For $B^{n}$ the $n$ -dimensional unit ball and $D_{n}$ its Siegel unbounded realization, we consider Toeplitz operators acting on weighted Bergman spaces with symbols invariant…

math.OA2024

Operator algebras and unitary representations of Polish groups

Raul Quiroga-Barranco

We study the relationship between operator algebras, $C^{*}$ and von Neumann, acting on a Hilbert space and unitary representations of topological groups on the same space. We obtain…

math.FA2023

The Heisenberg group action on the Siegel domain and the structure of Bergman spaces

Julio A. Barrera-Reyes, Raul Quiroga-Barranco

We study the biholomorphic action of the Heisenberg group $H_{n}$ on the Siegel domain $D_{n + 1}$ ( $n \geq 1$ ). Such $H_{n}$ -action allows us to obtain decompositions…

math.CV2023

Commuting Toeplitz operators and moment maps on Cartan domains of type III

David Cuevas-Estrada, Raul Quiroga-Barranco

Let $D_{n}^{I I I}$ and $S_{n}$ be the Cartan domains of type III that consist of the symmetric $n \times n$ complex matrices $Z$ that satisfy $Z Z < I_{n}$ and $\mathr…

math.FA2022

Commuting Toeplitz operators on Cartan domains of type IV and moment maps

Raul Quiroga-Barranco, Monyrattanak Seng

Let us consider, for $n \geq 3$ , the Cartan domain $D_{n}^{IV}$ of type IV. On the weighted Bergman spaces $A_{λ}^{2} (D_{n}^{IV})$ we study th…

math.FA2022

Radial-like Toeplitz operators on Cartan domains of type I

Raul Quiroga-Barranco

Let $D_{n \times n}^{I}$ be the Cartan domain of type I which consists of the complex $n \times n$ matrices $Z$ that satisfy $Z^{*} Z < I_{n}$ . For a symbol $a \in L^\in…

math.FA2021

Toeplitz operators, $T^{m}$ -invariance and quasi-homogeneous symbols

Raul Quiroga-Barranco

For a partition $k = (k_{1}, \dots, k_{m})$ of $n$ consider the group $U (k) = U (k_{1}) \times \dots \times U (k_{m})$ block diagonally e…

math.CV2020

Moment maps of Abelian groups and commuting Toeplitz operators acting on the unit ball

Raul Quiroga-Barranco, Armando Sanchez-Nungaray

We prove that to every connected Abelian subgroup $H$ of the biholomorphisms of the unit ball $B^{n}$ we can associate a set of bounded symbols whose corresponding Toeplitz…

math.DG2020

Local and global rigidity for isometric actions of simple Lie groups on pseudo-Riemannian manifolds

Raul Quiroga-Barranco

Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an isometric $G$ -action with a dense orbit, where $G$ is a connected non-compact simple Lie group. For lo…

math.FA2019

Toeplitz operators on the domain ${Z \in M_{2 \times 2} (C) ∣ Z Z^{*} < I}$ with $U (2) \times T^{2}$ -invariant symbols

Matthew Dawson, Gestur Olafsson, Raul Quiroga-Barranco

Let $D$ be the irreducible bounded symmetric domain of $2 \times 2$ complex matrices that satisfy $Z Z^{*} < I_{2}$ . The biholomorphism group of $D$ is realized by $U (2, 2)$ with…

cs.IT2019

Information geometry and asymptotic geodesics on the space of normal distributions

Wolfgang Globke, Raul Quiroga-Barranco

The family $N$ of $n$ -variate normal distributions is parameterized by the cone of positive definite symmetric $n \times n$ -matrices and the $n$ -dimensional real vector sp…

math.FA2018

Bicomplex Bergman spaces on bounded domains

Cesar O. Perez-Regalado, Raul Quiroga-Barranco

The bicomplex Bergman spaces are studied for any bounded bicomplex domain. Its Bergman kernel is computed in terms of the kernels of the complex projections of the domain. We also…

math.FA2018★ 1 cited

The Restriction Principle and Commuting Families of Toeplitz Operators on the Unit Ball

M. Dawson, G. Olafsson, R. Quiroga-Barranco

On the unit ball B^n we consider the weighted Bergman spaces H_λand their Toeplitz operators with bounded symbols. It is known from our previous work that if a closed subgroup H of…

math.FA2017

Radial Toeplitz operators on the weighted Bergman spaces of Cartan domains

Matthew Dawson, Raul Quiroga-Barranco

Let $D$ be an irreducible bounded symmetric domain with biholomorphism group $G$ with maximal compact subgroup $K$ . For the Toeplitz operators with $K$ -invariant symbols we provide…

math.FA2016

Toeplitz operators, pseudo-homogeneous symbols and moment maps on the complex projective space

Miguel Antonio Morales-Ramos, Raúl Quiroga-Barranco, Armando Sánchez-Nungaray

Following previous works for the unit ball, we define quasi-radial pseudo-homogeneous symbols on the projective space and obtain the corresponding commutativity results for Toeplit…

math.FA2016

Separately Radial and Radial Toeplitz Operators on the Projective Space and Representation Theory

R. Quiroga-Barranco, A. Sanchez-Nungaray

We consider separately radial (with corresponding group $T^{n}$ ) and radial (with corresponding group $U (n))$ symbols on the projective space $\mathbb{P}^n(\mathbb{…

math.DG2016

Rigidity of an Isometric $S L (3, R)$ -Action

Raul Quiroga-Barranco, Eli Roblero-Méndez

We characterize the universal covering of connected analytic pseudo-Riemannian manifolds which admit a non-trivial and isometric action of the simple Lie group $S L (3, R)$ w…

math.DG2015

Pseudo-Riemannian $G_{2 (2)}$ -manifolds with dimension at most $21$

R. Quiroga-Barranco

Let $G_{2 (2)}$ be the non-compact connected simple Lie group of type $G_{2}$ over $R$ , and let $M$ be a connected analytic complete pseudo-Riemannian manifold that admits an…

math.FA2015★ 1 cited

Separately Radial and Radial Toeplitz Operators on the Unit Ball and Representation Theory

Raul Quiroga-Barranco

We study Toeplitz operators with separately radial and radial symbols on the weighted Bergman spaces on the unit ball. The unitary equivalence of such operators with multiplication…

math.OA2015

Commutative $C^{*}$ -algebras generated by Toeplitz operators on the super unit ball

R. Quiroga-Barranco, A. Sánchez-Nungaray

We extend known results about commutative $C^{*}$ -algebras generated Toeplitz operators over the unit ball to the supermanifold setup. This is obtained by constructing commutative $C…

math.DG2015

On low-dimensional manifolds with isometric $U (p, q)$ -actions

Gestur Ólafsson, Raul Quiroga-Barranco

Denote by $U (p, q)$ the universal covering group of $U (p, q)$ , the linear group of isometries of the pseudo-Hermitian space $C^{p, q}$ of signat…

math.OA2014

Commuting Toeplitz Operators on Bounded Symmetric Domains and Multiplicity-Free Restrictions of Holomorphic Discrete Series

Matthew Dawson, Gestur Ólafsson, Raúl Quiroga-Barranco

For any given bounded symmetric domain, we prove the existence of commutative $C^{*}$ -algebras generated by Toeplitz operators acting on any weighted Bergman space. The symbols of th…

math.FA2014

Toeplitz Operators with Quasi-Homogeneuos Quasi-Radial Symbols on some Weakly Pseudoconvex Domains

Raul Quiroga-Barranco, Armando Sanchez-Nungaray

On the weakly pseudo-convex domains $Ω_{p}^{n}$ we introduce quasi-homogeneous quasi-radial symbols. These are used to prove the existence of a commutative Banach algebra of Toeplitz o…

Geometry of the slice regular Möbius transformations of the quaternionic unit ball

Toeplitz operators and group-moment coordinates for quasi-elliptic and quasi-hyperbolic symbols

Operator algebras and unitary representations of Polish groups

The Heisenberg group action on the Siegel domain and the structure of Bergman spaces

Commuting Toeplitz operators and moment maps on Cartan domains of type III

Commuting Toeplitz operators on Cartan domains of type IV and moment maps

Radial-like Toeplitz operators on Cartan domains of type I

Toeplitz operators, Tm-invariance and quasi-homogeneous symbols

Moment maps of Abelian groups and commuting Toeplitz operators acting on the unit ball

Local and global rigidity for isometric actions of simple Lie groups on pseudo-Riemannian manifolds

Toeplitz operators on the domain {Z∈M2×2​(C)∣ZZ∗<I} with U(2)×T2-invariant symbols

Information geometry and asymptotic geodesics on the space of normal distributions

Bicomplex Bergman spaces on bounded domains

The Restriction Principle and Commuting Families of Toeplitz Operators on the Unit Ball

Radial Toeplitz operators on the weighted Bergman spaces of Cartan domains

Toeplitz operators, pseudo-homogeneous symbols and moment maps on the complex projective space

Separately Radial and Radial Toeplitz Operators on the Projective Space and Representation Theory

Rigidity of an Isometric SL(3,R)-Action

Pseudo-Riemannian G2(2)​-manifolds with dimension at most 21

Separately Radial and Radial Toeplitz Operators on the Unit Ball and Representation Theory

Commutative C∗-algebras generated by Toeplitz operators on the super unit ball

On low-dimensional manifolds with isometric U(p,q)-actions

Commuting Toeplitz Operators on Bounded Symmetric Domains and Multiplicity-Free Restrictions of Holomorphic Discrete Series

Toeplitz Operators with Quasi-Homogeneuos Quasi-Radial Symbols on some Weakly Pseudoconvex Domains

Toeplitz operators, $T^{m}$ -invariance and quasi-homogeneous symbols

Toeplitz operators on the domain ${Z \in M_{2 \times 2} (C) ∣ Z Z^{*} < I}$ with $U (2) \times T^{2}$ -invariant symbols

Rigidity of an Isometric $S L (3, R)$ -Action

Pseudo-Riemannian $G_{2 (2)}$ -manifolds with dimension at most $21$

Commutative $C^{*}$ -algebras generated by Toeplitz operators on the super unit ball

On low-dimensional manifolds with isometric $U (p, q)$ -actions