The Automorphism Group of Certain Higher Degree Forms

On certain representations of automorphism groups of an algebraically closed field

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any non-faithful continuous representation of G factors through a discrete quotient of G. Properties of representation of G arising from geometry are studied. In some cases the groups of morphisms between geometric objects are identified with the groups of morphisms between corresponding G-modules, and the ${\rm Ext}^1$'s are related. In particular, the category of abeli…

On some rational extension properties for $GL_n(q)$ and even-degree characters fixed by order-2 Galois automorphisms

In this note, we prove that if every character of a finite group $G$ fixed by an order-2 Galois automorphism has odd degree, then $G$ has a normal Sylow $2$-subgroup. On the way, we study extensions of characters of $GL_n(q)$, $q$ odd, to the group extended by the transpose-inverse automorphism and prove that unipotent characters of $PSL_n(q)$ extend to rational characters of its automorphism group.

带图自同构作用的扭曲多圈代数的整基

Integral bases for twisted multiloop algebras with diagram automorphism actions

该研究针对带图自同构作用的扭曲多圈代数，构造了其泛包络代数的整形式及显式整基，解决了相关代数结构的整基存在性与构造问题。

有界上同调与正则树自同构群的酉表示

Bounded Cohomology and Unitary Representations of Automorphism Groups of Regular Trees

本文首次计算了正则树自同构群在所有正度数下的连续有界上同调，系数来自任何不可约连续酉表示。

Representations of field automorphism groups

This is a common introduction to math.RT/0101170, math.RT/0306333, math.RT/0506043, math.RT/0601028. Compared to these references there are new results including (i) a description of a separable closure of an extension of transcendence degree one of an algebraically closed field of positive characteristic; (ii) a "Künneth formula" for the products with curves; (iii) the semi-simplicity of the module of regular forms of top degree $Ω^n_{F/k}$.

某些 Kummer 曲面的自同构在模 $p$ 点上通过交错群作用

The automorphisms of certain Kummer surfaces act on the points mod $p$ by the alternating group

本文研究有限域上椭圆曲线平方的 Kummer 曲面自同构作用，证明其在点集上传递时作用至少为交错群，并类比了 Markoff 曲面的相关结果。