论文标题
特征值的斜率确定统一群体
Slopes in eigenvarieties for definite unitary groups
论文作者
论文摘要
我们将Liu-Wan-Xiao的界限概括为特征库中的斜率，以确定的统一群体$ 2 $ $ 2 $的斜坡，以在特征范围的斜坡上，以确定任何等级的统一群体。我们表明，对于一个确定的统一组$ n $，$ u_p $ hecke运营商的特征功率系列的牛顿多边形具有精确的增长率$ x^{1+\ frac2 {n（n-1）} $，与重量与重量空间边界的距离成比例不断成比例。证明涉及与主序列表示相关的形式的分类。我们还为这些特征值在重量空间的边界上的几何形状产生了后果。
We generalize bounds of Liu-Wan-Xiao for slopes in eigencurves for definite unitary groups of rank $2$ to slopes in eigenvarieties for definite unitary groups of any rank. We show that for a definite unitary group of rank $n$, the Newton polygon of the characteristic power series of the $U_p$ Hecke operator has exact growth rate $x^{1+\frac2{n(n-1)}}$, times a constant proportional to the distance of the weight from the boundary of weight space. The proof goes through the classification of forms associated to principal series representations. We also give a consequence for the geometry of these eigenvarieties over the boundary of weight space.
