arXiv subjects

Andrea Vera-Gajardo

Publications and source records attributed to Andrea Vera-Gajardo.

3 recordsLinked to original sources

arXiv2021

Now that we are together: Biography of the Chilean Collective of Women Mathematicians

In this article we propose to give an account of the history of the Chilean collective of women mathematicians. We will begin by describing the context of the mathematical community in Chile and the process of forming the Collective, together with the first objectives we set ourselves. Then we will continue with an analysis of some reasons that support the need to create a group formed by mathematical women and also the fact of choosing horizontality and autonomy as structural pillars of our organization. On the other hand, we will refer to the main activities that we have carried out and we will provide an overview of the mathematical women's organizations that exist in Latin America. Finally, we will conclude by talking about the research project to which some of the members of the collective are dedicated nowadays (in particular the authors of this article).

math.HO↗

arXiv2019

Representations of reductive groups over finite local rings of length two

Let $\mathbb{F}_{q}$ be a finite field of characteristic $p$, and let $W_{2}(\mathbb{F}_{q})$ be the ring of Witt vectors of length two over $\mathbb{F}_{q}$. We prove that for any reductive group scheme $\mathbb{G}$ over $\mathbb{Z}$ such that $p$ is very good for $\mathbb{G}\times\mathbb{F}_{q}$, the groups $\mathbb{G}(\mathbb{F}_{q}[t]/t^{2})$ and $\mathbb{G}(W_{2}(\mathbb{F}_{q}))$ have the same number of irreducible representations of dimension $d$, for each $d$. Equivalently, there exists an isomorphism of group algebras $\mathbb{C}[\mathbb{G}(\mathbb{F}_{q}[t]/t^{2})]\cong\mathbb{C}[\mathbb{G}(W_{2}(\mathbb{F}_{q}))]$.

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↗