On compatibility in restriction of Arthur's conjecture for $R$-groups

GSp $_4$的Arthur重数公式及对Sp $_4$的限制

Arthur's multiplicity formula for GSp$_4$ and restriction to Sp$_4$

我们证明了[Art04]中解释的GSp $_4$的离散自守表示的分类，以及GSp $_4$和Sp $_4$的局部Langlands对应之间的相容性。

关于Arthur表示与单位元双的关系

On Arthur representations and the unitary dual

本文提出一个关于Arthur表示与单位元双结构的新猜想，并通过算法和验证支持其完备性。

Branching laws for discrete series of some affine symmetric spaces

In this paper we study branching laws for certain unitary representations. This is done on the smooth vectors via a version of the {\it period integrals}, studied in number theory, and also closely connected to the {\it symmetry-breaking operators}, introduced by T.~Kobayashi. We exhibit non-vanishing symmetry breaking operators for the restriction of a representation $Π$ in the discrete spectrum for real hyperboloids to representations of smaller orthogonal groups. In the last part we discuss some conjectures for the restriction of representations in Arthur packets containing the representati…

关于函数域上的广义 Ramanujan 与 Arthur 猜想

On the generalized Ramanujan and Arthur conjectures over function fields

本文利用 V. Lafforgue 的 Galois 参数化和 Deligne 的 Frobenius 权重理论，证明了函数域上单群尖点自守表示在非分歧拟分裂位处的缓和性，结果与 Shahidi 和 Arthur 的广义猜想一致。

On restriction of unitarizable representations of general linear groups and the non-generic local Gan-Gross-Prasad conjecture

We prove one direction of a recently posed conjecture by Gan-Gross-Prasad, which predicts the branching laws that govern restriction from p-adic $GL_n$ to $GL_{n-1}$ of irreducible smooth representations within the Arthur-type class. We extend this prediction to the full class of unitarizable representations, by exhibiting a combinatorial relation that must be satisfied for any pair of irreducible representations, in which one appears as a quotient of the restriction of the other. We settle the full conjecture for the cases in which either one of the representations in the pair is generic. The…

Derivation functors and Lusztig's induction functors

Lusztig proved the compatibility of induction functors and restriction functors for Lusztig's perverse sheaves. Fang-Lan-Xiao established a categorification of Green's formula and gave a sheaf-level proof of this compatibility for all semisimple complexes. As an application, we study the relation between induction functors and derivation functors, which is a kind of special restriction functors.