On graded quotient modules of mapping class groups of surfaces
On graded quotient modules of mapping class groups of surfaces
复制标题
曲面映射类群的分级商模
DOI：
10.1007/bf02783208
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发表时间：
1995
影响因子：
1
通讯作者：
Hiroaki Nakamura
中科院分区：
文献类型：
--
作者：
Mamoru Asada;Hiroaki Nakamura
设Γg，n是保n点亏格的紧致Riemann曲面的映射类群（2−2g−n<0，g≥1，n≥0）.Γg，n的Torelli子群有自然权滤子{Γg，n（m）}m≥1.每个分次商grmΓg，n（m≥1）是群Sp（2g，n）× Sn自然作用于其上的有限维向量空间.本文确定了grmΓg，n（1≤m≤3）的Sp（2g，n）× Sn模结构.这包括S对期望的验证。森田对于一般模，通过显式构造这些模中的元素，我们确定了grmΓg，n的一个Sp（2g，n）-不可约分支.
Let Γg, nbe the mapping class group of a compact Riemann surface of genusgwithnpoints preserved (2−2g−n<0,g≥1,n≥0). The Torelli subgroup of Γg, nhas a natural weight filtration {Γg, n(m)}m≥1. Each graded quotient grmΓg, n⊗ ℚ (m≥1) is a finite dimensional vector space over ℚ on which the group Sp(2g, ℚ)×Snnaturally acts.In this paper, we have determined the Sp(2g, ℚ)×Snmodule structure of grmΓg, n⊗ ℚ for 1≤m≤3. This includes a verification of an expectation by S. Morita. Also, for generalm, we have identified a certain Sp(2g, ℚ)-irreducible component of grmΓg, n⊗ ℚ by constructing explicitly elements in these modules.