论文标题
Schur-weyl二元性和较高的Abel-Jacobi不变式的重言式周期$ \ Mathcal {m} _ {g，n} $
Schur-Weyl Duality and Higher Abel-Jacobi Invariants for Tautological Cycles in $\mathcal{M}_{g,n}$
论文作者
论文摘要
本文研究了带有$ n $标记点的属属属属的模量空间的Hodge理论，并在$ \ Mathfrak {sp} _ {g} $和更高的Abel-Jacobi Infformiants之间建立了新的联系。我们开发了一个represe \\ ntation thoretic框架，该框架分解了$ c_ {g}^{n} $在$ c_ {g}^{n} $中的较高的Abel-Jacobi不变式，该框架根据symplectic lie代表表示，利用$ \ \ \ \ \ \ \ \ \ {SP} c} c} Central to this work is the introduction of \textbf{higher Faber-Pandharipande cycles} $FP_n = π_1^{\times 2}(Δ_{12}^n \cdot ψ_1)$ in $CH^{n+1}(C_g^2)$, a new family of tautological cycles generalizing classical constructions.我们证明，在最佳属约束下，这些周期是非扭转的：对于$（n-1）$ - 尺寸基础的家庭，$ fp_n $在$ g \ geq 3n+1 $时并不等于零。此外，我们确定$ fp_n $在$ c_g^2 \ to m_g $的LERAY过滤中的确切位置，显示它在深度$ n+1 $中，但没有更深的深度，并且在$ H^{n+1}中明显不呈nothishing，n+1} $ v _ {（n+1,1）} $ - 同种型组件。这产生了Schur-Weyl二元性与较高的先验不变性之间的第一个系统联系，表明较高的对角线编码标准重言式术类别看不见的几何现象。
This article investigates the Hodge theory of the moduli space of genus $g$ curves with $n$ marked points, establishing new connections between Schur-Weyl duality for $\mathfrak{sp}_{g}$ and higher Abel-Jacobi invariants. We develop a represe\\ ntation-theoretic framework that decomposes higher Abel-Jacobi invariants of tautological cycles in $C_{g}^{n}$ according to symplectic Lie algebra representations, leveraging the Leray filtration and motivic decompositions compatible with $\mathfrak{sp}_{2g}$-actions. Central to this work is the introduction of \textbf{higher Faber-Pandharipande cycles} $FP_n = π_1^{\times 2}(Δ_{12}^n \cdot ψ_1)$ in $CH^{n+1}(C_g^2)$, a new family of tautological cycles generalizing classical constructions. We prove these cycles are non-torsion under optimal genus constraints: for families over $(n-1)$-dimensional bases, $FP_n$ is not rationally equivalent to zero when $g \geq 3n+1$. Furthermore, we determine the precise position of $FP_n$ in the Leray filtration of $C_g^2 \to M_g$, showing it lies in depth $n+1$ but no deeper, with explicit non-vanishing in $H^{n+1}(M_g, R^{n+1}f_*\mathbb{Q})$ on the $V_{(n+1,1)}$-isotypic component. This yields the first systematic link between Schur-Weyl duality and higher transcendental invariants, revealing that higher diagonals encode geometric phenomena invisible to standard tautological classes.
