arXiv subjects

Huajian Xue

Publications and source records attributed to Huajian Xue.

4 recordsLinked to original sources

arXiv2023

Full theta lifting for type II reductive dual pairs

In this article, we study the full theta lifting for two cases of type II reductive dual pairs over a nonarchimedean local field. Firstly, we determine the structure of the full theta lifts of all irreducible representations for dual pair $(\mathrm{GL}(2),\mathrm{GL}(2))$. Secondly, we prove that the full theta lift of an irreducible tempered representation is irreducible and tempered for dual pair $(\mathrm{GL}(n),\mathrm{GL}(n+1))$, where $n$ is a positive integer.

math.RT↗

arXiv2017

Godement-Jacquet L-functions and full theta lifts

We relate poles of local Godement-Jacquet L-functions to distributions on matrix spaces with singular supports. As an application, we show the irreducibility of the full theta lifts to $GL_n(F)$ of generic irreducible representations of $GL_n(F)$, where $F$ is an arbitrary local field.

math.RT↗

arXiv2016

On the nonvanishing hypothesis for Rankin-Selberg convolutions for $\mathrm{GL}_n(\mathbb C)\times \mathrm{GL}_n(\mathbb C)$

Inspired by Sun's breakthrough in establishing the nonvanishing hypothesis for Rankin-Selberg convolutions for the groups $\mathrm{GL}_n (\mathbb R)\times \mathrm{GL}_{n-1} (\mathbb R)$ and $\mathrm{GL}_n (\mathbb C)\times \mathrm{GL}_{n-1} (\mathbb C)$, we confirm it for $\mathrm{GL}_{n} (\mathbb C)\times \mathrm{GL}_n (\mathbb C)$ at the central critical point.

math.RT↗

arXiv2016

Homogeneous distributions on finite dimensional vector spaces

Let $V$ be a finite dimensional vector space over a local field $F$. Let $χ: F^\times \rightarrow \mathbb C^\times$ be an arbitrary character of $F^\times$. We determine the structure of the natural representation of $\mathrm{GL}(V)$ on the space $\mathcal{S}^*(V)^χ$ of $χ$-invariant distributions on $V$.

math.RT↗