标题： 通过映射类群和自由群自同构群的同余子群的一阶同调来表示模形式 显示英文标题

标题： Modular representations via the first homology of congruence subgroups of mapping class groups and automorphism groups of free groups

摘要： 我们研究了从映射类群和自由群自同构群的同余子群的第一同调以及托里利群的交换化之不变量模的首阶同调中得到的辛群和特殊线性群在有限域上的模表示序列。 在所有情况下，我们计算了这些表示的合成因子及其重数，并在Church--Farb的意义下获得了周期性的表示稳定性结果。 显示英文摘要

摘要： We study sequences of modular representations of the symplectic and special linear groups over finite fields obtained from the first homology of congruence subgroups of mapping class groups and automorphism groups of free groups, and the module of coinvariants for the abelianization of the Torelli group. In all cases we compute the composition factors and multiplicities for these representations, and obtain periodic representation stability results in the sense of Church--Farb.