辛型标准$L$-函数的周期关系

On Symplectic Periods for Inner forms of ${\rm GL}_n$

In this paper we study the question of determining when an irreducible admissible representation of ${\rm GL}_n(D)$ admits a symplectic model, that is when such a representation has a linear functional invariant under ${\rm Sp}_n(D)$, where $D$ is a quaternion division algebra over a non-Archimedian local field $k$ and ${\rm Sp}_{n}(D)$ is the unique non-split inner form of the symplectic group ${\rm Sp}_{2n}(k)$. We show that if a representation has a symplectic model it is necessarily unique. For ${\rm GL}_2(D)$ we completely classify those representations which have a symplectic model. Glob…

四元数GL_n(D)的离散级数表示与辛周期

Discrete series representations of quaternionic ${\rm GL}_n(D)$ with symplectic periods

本文研究了四元数GL_n(D)的离散级数表示，证明了其具有辛周期当且仅当该表示是本原的，并且其Jacquet-Langlands转移至GL_{2n}(F)时是非本原的。

关于辛群的剩余自守表示与周期积分

On residual automorphic representations and period integrals for symplectic groups

本文构造了辛群离散自守谱中的新不可约分支，将具有线性周期的 GL_{2n} 尖点自守表示提升为任意秩 k≥2n 辛群的剩余表示，并证明其存在非零不变线性型，推广了下降法中的经典构造。

Petersson 内积与偶特殊正交群和辛群上的 Whittaker--Fourier 周期

Petersson Inner Products and Whittaker--Fourier Periods on Even Special Orthogonal and Symplectic Groups

本文在偶特殊正交群和辛群上建立 Whittaker--Fourier 系数平方范数与 Petersson 内积及 $L$-函数临界值的关系，并给出奇特殊正交群的类似结果。

Periods and $(χ,b)$-factors of Cuspidal Automorphic Forms of Symplectic Groups

In this paper, we introduce a new family of period integrals attached to irreducible cuspidal automorphic representations $σ$ of symplectic groups $\mathrm{Sp}_{2n}(\mathbb{A})$, which detects the right-most pole of the $L$-function $L(s,σ\timesχ)$ for some character $χ$ of $F^\times\backslash\mathbb{A}^\times$ of order at most $2$, and hence the occurrence of a simple global Arthur parameter $(χ,b)$ in the global Arthur parameter $ψ$ attached to $σ$. We also give a characterisation of first occurrences of theta correspondence by (regularised) period integrals of residues of certain Eisenstein…

Relations among smooth integral models associated to quadratic, symplectic and hermitian lattices

This work is motivated by an investigation into whether, and if so how, certain well known facts about Lie groups manifest in the context of group schemes over rings of integers of local fields. There are the following well-known relations among unitary, orthogonal and symplectic groups: U(n)=O(2n) \cap GL(n, C)=Sp(2n) \cap GL(n, C). Therefore, it is natural to ask whether or not there exist such relations among smooth integral models of unitary, orthogonal and symplectic groups defined over a local field. Moreover, if there do not exist such relations, it would still be worthwhile if one can …