论文标题
关于Kac-Moody Eisenstein系列的收敛
On the convergence of Kac-Moody Eisenstein series
论文作者
论文摘要
令$ g $为与非对称性概括的cartan矩阵相关的表示形式理论kac-moody群体。我们首先考虑了Borel Eisenstein系列的Kac-Moody类似物（由Borel上的Quasicharacters诱导），并证明它们几乎在山雀锥体内的任何地方都融合了神谱的任意光谱参数。然后，我们使用此结果来显示一类满足某种组合特性的KAC-MOODY群体，特别是对于Rank-2双曲线组，山雀锥内部的全部绝对收敛（再次用于神范围内的光谱参数）。
Let $G$ be a representation-theoretic Kac--Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We first consider Kac-Moody analogs of Borel Eisenstein series (induced from quasicharacters on the Borel), and prove they converge almost everywhere inside the Tits cone for arbitrary spectral parameters in the Godement range. We then use this result to show the full absolute convergence everywhere inside the Tits cone (again for spectral parameters in the Godement range) for a class of Kac-Moody groups satisfying a certain combinatorial property, in particular for rank-2 hyperbolic groups.
