论文标题
通过颤抖表示的多谐和麦形式的分类
A classification of polyharmonic Maaß forms via quiver representations
论文作者
论文摘要
我们将回购生成的harish-chandra模块分类为\ emph {poly}的谐波maaß形式的〜$ \ sl {2}（\ rr）$，用于〜$ \ sl {2}（2}（\ zz）$的一致性子组，允许在Cusps实用指定增长。这扩展了Bringmann-kudla在谐波案例中的结果。在谐波环境中有9例案例，我们的分类包括十个；一个新案例以$ k> 1 $出现。为了获得分类，我们将颤抖的表示形式介绍到该主题中，并表明与多结式Maaß形式相关的那些是循环的，不可分解的是两循环或Gelfand Quiver的代表。 将这些转移分类为多谐波弱maas形式的分类。为了实现Harish-Chandra模块的所有可能案例，我们开发了一种体重转移理论，用于矢量值谱系家族的泰勒系数。我们提供了该理论的全面计算机实施，这使我们能够提供明确的示例。
We give a classification of the Harish-Chandra modules generated by the pullback to~$\SL{2}(\RR)$ of \emph{poly}harmonic Maaß forms for congruence subgroups of~$\SL{2}(\ZZ)$ with exponential growth allowed at the cusps. This extends results of Bringmann--Kudla in the harmonic case. While in the harmonic setting there are nine cases, our classification comprises ten; A new case arises in weights $k > 1$. To obtain the classification we introduce quiver representations into the topic and show that those associated with polyharmonic Maaß forms are cyclic, indecomposable representations of the two-cyclic or the Gelfand quiver. A classification of these transfers to a classification of polyharmonic weak Maaß forms. To realize all possible cases of Harish-Chandra modules we develop a theory of weight shifts for Taylor coefficients of vector-valued spectral families. We provide a comprehensive computer implementation of this theory, which allows us to provide explicit examples.
