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Luis Gutiérrez Frez

Publications and source records attributed to Luis Gutiérrez Frez.

8 recordsLinked to original sources
arXiv2026

Black holes and phase transitions in Conformal Gravity

We explore the thermodynamic properties of static black holes in conformal gravities in arbitrary, even dimensions. In the spherically symmetric case, up to local Weyl rescalings, these spacetimes are static and unique, due to a Birkhoff's theorem that applies for all conformal gravities whose Lagrangians are complete contractions of $k$ Weyl tensors in dimension $D=2k$. The solutions can be chosen to be asymptotically locally (A)dS or flat, and the horizon can be extended to be a surface of arbitrary constant curvature, $γ$. We focus on the asymptotically AdS case, for which the cosmological constant at infinity is an integration constant, and compute the mass of the spacetime in terms of the diverse hair parameters which have a purely gravitational origin. We show that the first law of thermodynamics is satisfied, and study phase transitions in the canonical ensemble, showing the existence of zeroth-order black-hole/black-hole phase transitions for arbitrary dimension.

hep-th↗
arXiv2025

Classifying representations of finite classical groups of Lie type of dimension up to $\ell^4$

Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to $\ell$, and splits into two cases according to $G$ is of type $A_{\ell}$ or not. Furthermore, we discuss explicit formulas for computing the dimensions of such representations. The motivation for this work arises, in part, from a desire to obtain new results on two classical problems concerning Galois representations: the large image conjecture for automorphic Galois representations and the inverse Galois problem. We conclude the paper by giving some remarks on potential implications in these addresses.

math.RT↗
arXiv2024

Typical representations for $\mathrm{Sp}_4(F)$

Let $F$ be a non Archimedean local field with odd residual characteristic, and let $K$ be a hyperspecial maximal compact subgroup of the $p$-adic symplectic group $G=\mathrm{Sp}_4(F)$. Let $\mathfrak{s}$ be an inertial class for $G$ in the Bernstein decomposition of the category of smooth representations of $G$, which is attached to a proper Levi subgroup $L$ of $G$. We prove that the $\mathfrak{s}$-typical irreducible representations of $K$ are the irreducible components of $\mathrm{Ind}_{J_{\mathfrak{s}}}^{K}(λ_{\mathfrak{s}})$, where $(J_{\mathfrak{s}},λ_{\mathfrak{s}})$ is an $\mathfrak{s}$-type for $G$ such that $J_{\mathfrak{s}}\subset K$, and $(J_{\mathfrak{s}},λ_{\mathfrak{s}})$ is a $G$-cover of a Bushnell-Kutzko maximal simple type for $L$.

math.RT↗
arXiv2021

${\rm SL}_*$ over local and adèle rings: $*$-euclideanity and Bruhat generators

Let $(R,*)$ be a ring with involution and let $A = {\rm M}(n,R)$ be the matrix ring endowed with the $*$-transpose involution. We study ${\rm SL}_*(2,A)$ and the question of Bruhat generation over commutative and non-commutative local and adèlic rings $R$. An important tool is the property of a ring being $*$-Euclidean. In this regard, we introduce the notion of a $*$-local ring $R$, prove that $A$ is $*$-Euclidean and explore reduction modulo the Jacobson radical for such rings. Globally, we provide an affirmative answer to the question wether a commutative adèlic ring $R$ leads towards the ring $A$ being $*$-Euclidean; while the non-commutative adèlic quaternions are such that $A$ is $*$-Euclidean and ${\rm SL}_*$ is generated by its Bruhat elements if and only if the characteristic is $2$.

math.GR↗
arXiv2019

Weil representations via abstract data and Heisenberg groups: a comparison

Let $B$ be a ring, not necessarily commutative, having an involution $*$ and let ${\mathrm U}_{2m}(B)$ be the unitary group of rank $2m$ associated to a hermitian or skew hermitian form relative to $*$. When $B$ is finite, we construct a Weil representation of ${\mathrm U}_{2m}(B)$ via Heisenberg groups and find its explicit matrix form on the Bruhat elements. As a consequence, we derive information on generalized Gauss sums. On the other hand, there is an axiomatic method to define a Weil representation of ${\mathrm U}_{2m}(B)$, and we compare the two Weil representations thus obtained under fairly general hypotheses. When $B$ is local, not necessarily finite, we compute the index of the subgroup of ${\mathrm U}_{2m}(B)$ generated by its Bruhat elements. Besides the independent interest, this subgroup and index are involved in the foregoing comparison of Weil representations.

math.RT↗
arXiv2016

Weil representations of $U(n,n)(\mathbb{F}_{q^2}/\mathbb{F}_q)$, $q>3$ odd via presentation and compatibility of methods

In this article we construct Weil representations of quasi-split unitary groups $U(n,n)(\mathbb{F}_{q^2}/\mathbb{F}_q)$ associated to quadratic extensions of finite fields. We define these representations by using an adequate presentation Bruhat like of those groups. More precisely, we define Weil representations of $U(n,n)(\mathbb{F}_{q^2}/\mathbb{F}_q)$ associating to each generator a linear map of a suitable $\mathbb{C}$-vector space satisfying the relations of the aforementioned presentation. In addition, we also address the natural question on the compatibility of our representation of $U(n,n)(\mathbb{F}_{q^2}/\mathbb{F}_q)$ with the classical one constructed by Gérardin.

math.RT↗
arXiv2015

Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution

We construct a complex linear Weil representation $ρ$ of the generalized special linear group $G={\rm SL}_*^{1}(2,A_n)$ ($A_n=K[x]/\langle x^n\rangle$, $K$ the quadratic extension of the finite field $k$ of $q$ elements, $q$ odd), where $A_n$ is endowed with a second class involution. After the construction of a specific data, the representation is defined on the generators of a Bruhat presentation of $G$, via linear operators satisfying the relations of the presentation. The structure of a unitary group $U$ associated to $G$ is described. Using this group we obtain a first decomposition of $ρ$.

math.RT↗