论文标题
通过（基本）代数几何形状的有限基团的表示理论
Representation theory of finite groups through (basic) algebraic geometry
论文作者
论文摘要
我们介绍了一种新方法来代表有限群体的理论，该理论使用一些基本的代数几何形状，并允许在不使用字符的情况下完成所有理论。通过这种方法，对于任何有限的组$ g $，我们都将有限数量的积分关联，并表明包含这些点坐标的任何字段都可以作为$ g $的表示形式的地面。我们将此观点应用于对称组$ s_d $，在$ d $变量中找到函数不同对称的简单方程式。作为副产品，我们简单地证明了Tocino的最新结果，该结果指出，除两种类型的对称性外，所有类型的对称性的超确定矩阵的超确定矩阵的超确定因素为零。
We introduce a new approach to representation theory of finite groups that uses some basic algebraic geometry and allows to do all the theory without using characters. With this approach, to any finite group $G$ we associate a finite number of points and show that any field containing the coordinates of those points works fine as the ground field for the representations of $G$. We apply this point of view to the symmetric group $S_d$, finding easy equations for the different symmetries of functions in $d$ variables. As a byproduct, we give an easy proof of a recent result by Tocino that states that the hyperdeterminant of a $d$-dimensional matrix is zero for all but two types of symmetry.
