自守剩余谱的一个简单构造
A simple construction of the automorphic residual spectrum
浏览论文内容
中文总结 AI 辅助
该研究针对数域上分裂半单线性代数群，通过正则化球Borel Eisenstein级数，遵循Kazhdan和Okounkov的哲学，结合等变积分公式证明其满足朗兰兹平方可积准则，进而给出Arthur幺正猜想的简单统一证明。
中文摘要 AI 辅助
我们考虑从数域上的分裂半单线性代数群的平凡表示诱导的球Borel Eisenstein级数。我们证明，其在对应于朗兰兹对偶李代数中一个特殊余伴随幂零轨道的半加权标记的特殊点处的正则化非零且平方可积。我们的证明遵循Kazhdan和Okounkov的哲学。我们在该设定下给出朗兰兹平方可积准则的几何解释，并利用等变积分公式证明该正则化满足此准则。作为直接结果，我们得到Arthur幺正猜想的一个简单且统一的证明，无需逐案分析或机器计算。
英文摘要
We consider the spherical Borel Eisenstein series induced from the trivial representation for a split semisimple linear algebraic group over a number field. We prove that its regularization at the special point corresponding to half the weighted marking of a distinguished coadjoint nilpotent orbit in the Langlands dual Lie algebra is nonzero and square-integrable. Our proof follows the philosophy of Kazhdan and Okounkov. We give a geometric interpretation of Langlands' square-integrability criterion in this setting and, using the equivariant integration formula, prove that the regularization satisfies this criterion. As an immediate consequence, we obtain a simple and uniform proof of Arthur's unitarity conjecture, without case-by-case analysis or machine computation.
