Double Descent in Classical Groups

Descents of unipotent cuspidal representations of finite classical groups

Inspired by the Gan-Gross-Prasad conjecture and the descent problem for classical groups, in this paper we study the descents of unipotent cuspidal representations of orthogonal and symplectic groups over finite fields.

Twisted descent algebras and the Solomon-Tits algebra

The purpose of the present article is to define and study a new class of descent algebras, called twisted descent algebras. These algebras are associated to the Barratt-Joyal theory of twisted bialgebras in the same way than classical descent algebras are associated to classical bialgebras. The formal properties of twisted descent algebras seem particularly meaningful in view of applications to discrete probabilities, to the geometry of Coxeter groups and buildings, and to symmetric group combinatorics.

Descents of unipotent representations of finite unitary groups

Inspired by the Gan-Gross-Prasad conjecture and the descent problem for classical groups, in this paper we study the descents of unipotent representations of unitary groups over finite fields. We give the first descents of unipotent representations explicitly, which are unipotent as well. Our results include both the Bessel case and Fourier-Jacobi case, which are related via theta correspondence.

闭合轨道与降阶在经典群增强标准表示中的应用

Closed Orbits and Descents for Enhanced Standard Representations of Classical Groups

本文研究了经典群在增强标准表示中的闭合轨道分类，确定了其稳定性及稳定化群作用。

经典李群的部分旗概形上线丛的半整性

Half-integrality of line bundles on partial flag schemes of classical Lie groups

本文发展部分旗概形上等变线丛的 Galois 下降理论，考察抛物子群特征所附下降数据分类的计算问题，并据此分类经典李群标准 $\mathbb{Z}[1/2]$-形式上的等变线丛。