Character sums associated to finite Coxeter groups

Coxeter型深层Deligne--Lusztig表示

Deep level Deligne--Lusztig representations of Coxeter type

本文通过研究局部非阿基米德域上约化群的Coxeter型深层Deligne--Lusztig簇上同调，构造了p进群抛物子群的新不可约表示，并在拟分裂情形下证明其紧诱导为超尖点表示直和，扩展了相关研究结果。

Cohomological invariants of finite Coxeter groups

In this paper, we generalize Serre's splitting theorem for cohomological invariants of the symmetric group to finite Coxeter groups, provided that the ground field has characteristic zero. We then use this principle to determine all the cohomological invariants of Weyl groups of classical type with coefficients modulo 2.

万花筒、波与预势

Kaleidoscopes, Waves and the Prepotential

本文通过研究同构flops对应的Coxeter群对称性，构造了Kähler有利CICYs中所有Coxeter对称性的数据库，并利用Laplace-Beltrami算子的本征函数对预势进行重求和，以加速模空间内部世界片瞬子贡献的收敛。

When is the ring of $T$ invariants of the homogeneous coordinate ring of $G/B$ a polynomial algebra- connection with the Coxeter elements

In this article, we prove that for any indecomposable dominant character of a maximal torus $T$ of a simple adjoint group $G$ such that there is a Coxeter element $w \in W$ for which $X(w)^{ss}_T(\mathcal L_χ) \neq \emptyset$. If further, for any dominant character $χ_1$ of $T$ such that $χ_1\lneqq χ$ with respect to the dominant ordering, $dim(H^0(G/B, \mathcal L_{χ_1})^T) < dim (H^0(G/B, \mathcal L_χ)^T)$, then the graded algebra $\oplus_{d \in \mathbb Z_{\geq 0}}H^0(G/B, \mathcal L_χ^{\otimes d})^T$ is a polynomial ring in $r$ variables where $r\geq 2$.

Stratification for multiplicative character sums

We prove a stratification result for certain families of $n$-dimensional (complete algebraic) multiplicative character sums. The character sums we consider are sums of products of $r$ multiplicative characters evaluated at rational functions, and the families (with $nr$ parameters) are obtained by allowing each of the $r$ rational functions to be replaced by an "offset", i.e. a translate, of itself. For very general such families, we show that the stratum of the parameter space on which the character sum has maximum weight $n+j$ has codimension at least $j\lfloor(r-1)/2(n-1)\rfloor$ for $1\le …

$A_1$ - 有限域上的库仑分支与塞尔伯格特征和

$A_1$ - Coulomb branches over finite fields and Selberg Character sums

该研究受镜像对称启发，通过多项式高斯和实现塞尔伯格特征和的几何化，结合埃文斯的结果得到有限域上$A_1$库仑分支指数和的显式公式。