发表机构
Nanjing University of Science and Technology; University of Mississippi（南京理工大学; 密西西比大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对Weyl交错式建立根向振荡抵消界，推广至混合导数，并应用于球函数与紧群特征标，恢复并细化已知逐点界。
AI 中文摘要
对于具有Weyl群$W$的约化晶体根系，Weyl交错式是由$W$指标化的指数函数的带符号和。它们出现在Weyl特征标公式的分子以及复半单群上球函数的显式公式中。我们建立了根向界，以量化这些振荡和中的抵消，每个正根贡献一个因子，该因子依赖于空间变量和谱参数。更一般地，我们为归一化Weyl交错式的所有混合方向导数建立了根向界。我们的证明将第二作者用于$\u200b\u200bSU(3)$上逐点特征标界的下降策略推广到任意秩。关键要素包括Weyl群分解为抛物双陪集以及相对BGG--Demazure恒等式。对于复半单群上的球函数，这些估计恢复了Brumley、Marshall、Matz和Peterson最近的逐点界，并通过在空间和谱根超平面上一致地控制任意混合径向导数，细化了Cowling和Nevo的导数界。此外，通过相对于仿射Weyl排列的标准局部化论证，我们为紧致连通半单群的不可约特征标建立了正则整权重的周期交错式估计，以及所有混合径向导数的相应根向界。
英文摘要
For a reduced crystallographic root system with Weyl group $W$, Weyl alternants are signed sums of exponentials indexed by $W$. They occur in the numerators of the Weyl character formula and the explicit formula for spherical functions on complex semisimple groups. We establish rootwise bounds that quantify cancellation in these oscillatory sums, with each positive root contributing a factor depending on both the spatial variable and the spectral parameter. More generally, we establish rootwise bounds for all mixed directional derivatives of normalized Weyl alternants. Our proof extends to arbitrary rank the descent strategy used by the second author for pointwise character bounds on $\mathrm{SU}(3)$. The key ingredients include the decomposition of the Weyl group into parabolic double cosets and the relative BGG--Demazure identity. For spherical functions on complex semisimple groups, these estimates recover the recent pointwise bound of Brumley, Marshall, Matz, and Peterson, and they refine the derivative bounds of Cowling and Nevo by controlling arbitrary mixed radial derivatives uniformly across spatial and spectral root hyperplanes. Furthermore, by a standard localization argument relative to the affine Weyl arrangement, we establish periodic alternant estimates for regular integral weights and corresponding rootwise bounds for all mixed radial derivatives of irreducible characters of compact connected semisimple groups.
Comments36 pages. Comments are welcome!
