arXiv subjects

Marcela Hanzer

Publications and source records attributed to Marcela Hanzer.

9 recordsLinked to original sources

arXiv2025

On the Mui\'c conjecture--the irreducibility of the big theta lift

Let $F$ be a non-archimedean local field of characteristic zero. We study theta correspondence for (complex) representations of symplectic--even orthogonal dual reductive pairs over $F;$ more specifically, the big theta lifts. We prove that, starting from a discrete series representation $\pi$ of a symplectic (even orthogonal group) over $F,$ its big theta lift $\Theta (\pi)$ (as a representation of an even orthogonal (symplectic) group) if non-zero, is an irreducible representation, thus proving a conjecture of Mui\'c. Building upon this result, we completely describe the situations in which the theta lifts of tempered representations are irreducible and when they are not.

math.RT↗

arXiv2024

Multiplicity free Weil representations arising from exceptional groups

Using exceptional theta correspondences, we prove that certain Weil representations of $p$-adic groups are multiplicity free and determine irreducible quotients.

math.RT↗

arXiv2022

Theta correspondence and Arthur packets: on the Adams conjecture

The Adams conjecture predicts that the local theta correspondence should respect Arthur packets. In this paper, we revisit the Adams conjecture for the symplectic--even orthogonal dual pair. Our results provide a precise description of all situations in which the conjecture holds.

math.RT↗

arXiv2019

Theta correspondence for symplectic-orthogonal and metaplectic-orthogonal p-adic dual pairs

In this paper, we completely describe the Howe correspondence for the dual pairs from the title over a nonarchimedean local field of characteristic zero. More specifically, for every irreducible admissible representation of these groups, we find its first occurrence index in the theta correspondence and we describe, in terms of their Langlands parameters, the small theta lifts on all levels.

math.RT↗

arXiv2019

Generic representations of metaplectic groups and their theta lifts

In this paper we give the description of generic representations of metaplectic groups over p-adic fields in terms of their Langlands parameters and calculate their theta lifts on all levels for any tower of odd orthogonal groups. We also describe precisely all the occurrences of the failure of the standard module conjecture for metaplectic groups.

math.RT↗

arXiv2018

Eisenstein series arising from Jordan algebras

We describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.

math.RT↗

arXiv2014

Generalized Shalika model on $\mathrm{SO}_{4n}(F),$ symplectic linear model on $\mathrm{Sp}_{4n}(F)$ and theta correspondence

We show that if an irreducible admissible representation of $\mathrm{SO}_{4n}(F)$ has a generalized Shalika model, then its small theta lift to $\mathrm{Sp}_{4n}(F)$ has the symplectic linear model, thus answering a question posed by D. Jiang. Here $F$ is a non-archimedean field of characteristic zero.

math.RT↗

arXiv2013

Degenerate Eisenstein Series for $Sp_4$

In this paper we obtain a complete description of images and poles of degenerate Eisenstein series attached to maximal parabolic subgroups of $Sp_4(\mathbb A)$, where $\mathbb A$ is the ring of adeles of $\mathbb Q$.

math.NT↗

arXiv2013

On the images and poles of degenerate Eisenstein series for $GL_n(\mathbb A_{\mathbb Q})$ and $GL_n(\mathbb R)$

I this paper we determine poles in the right--half plane and images of degenerate Eisenstein series for $GL_n(\Bbb A_\mathbb Q)$ induced from a character on a maximal parabolic subgroup. We apply those results to determine poles of degenerate Eisenstein series for $GL_n(\Bbb R)$.

math.NT↗