Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2305.19281

The Uniqueness of the Ginzburg-Rallis Model: the Non-Archimedean Case

Dihua Jiang·Zhaolin Li·Guodong Xi
View original source ↗Read source document ↗Export metadata ↓

Abstract

We prove the uniqueness of the Ginzburg-Rallis models over $p$-adic local fields of characteristic zero, which completes the local uniqueness problem for the Ginzburg-Rallis models starting from the work of C.-F. Nien in \cite{MR2709083} that proves the non-split case, and the work of D. Jiang, B. Sun and C. Zhu in \cite{MR2763736} that proves the general case over Archimedean local fields. Our proof extends the strategy of \cite{MR2763736} to the $p$-adic case with the help of the refined structure of the wavefront sets of $\mathfrak {z}$-finite distributions as developed by A. Aizenbud, D. Gourevitch and E. Sayag in \cite{MR3406530}.

Explore related subjects

math.RT

Keep this discovery

BibTeXRIS

Dihua Jiang, Zhaolin Li, Guodong Xi. 2023-05-27. The Uniqueness of the Ginzburg-Rallis Model: the Non-Archimedean Case. https://arxiv.org/abs/2305.19281

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Whittaker supermodules over Lie superalgebras

In this paper, we develop a general theory of quasi-Whittaker supermodules over Lie superalgebras induced from an arbitrary ideal. We determine the quasi-Whittaker vectors in universal supermodules, establish an irreducibility criterion, and classify several families of irreducible supermodules. The odd part produces a new irreducibility phenomenon absent from the Lie algebra setting. As applications, we determine all irreducible quasi-Whittaker supermodules over the $N=1$ super Schr\"odinger algebra and the $N=1$ $\frac{3}{2}$-conformal Galilei superalgebra, and over the complete spectrum-generating superalgebra in a special case.

math.RT↗
arXiv2026

Rankin--Selberg integrals of opposite conductor--one newforms

Let $F$ be a nonarchimedean local field of characteristic zero and let $n\geq2$. For $r=n,n+1$, let $\Pi_r$ be an irreducible tempered representation of ${\rm GL}_r(F)$ of conductor one and with trivial central character. We evaluate the Rankin--Selberg integral of opposite newforms in $\Pi_{n+1}\times \Pi_n$ explicitly and show that its central value is nonzero. As an application, this implies a case of Disegni--Zhang's conjecture on the nonvanishing of local relative characters.

math.RT↗
arXiv2026

Obstructions to Jacobi-Finiteness of Quivers with Potentials

We show that Jacobi-finite potentials need not exist on finite $2$-acyclic quivers. Our main tool is a matrix-valued Golod--Shafarevich--Vinberg inequality for quotients of completed path algebras by finitely many, possibly nonhomogeneous, topological relations. Applied to cyclic derivatives, it yields a potential-dependent obstruction to the finite-dimensionality of completed Jacobian algebras. We then construct a purely quiver-level criterion excluding every Jacobi-finite potential on a given quiver, and exhibit a family of quivers for which every potential has an infinite-dimensional Jacobian algebra.

math.RT↗