仿杨代数$Y_{t_1,t_2}(\boldsymbol{\text{gl}}_1)$在曲面上稳定层模空间上同调中的作用
An action of the affine Yangian $Y_{t_1,t_2}(\widehat{\mathfrak{gl}}_1)$ on the cohomology of the moduli space of stable sheaves on surfaces
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中文总结 AI 辅助
该数学研究证明了仿杨代数$Y_{t_1,t_2}(\boldsymbol{\text{gl}}_1)$在光滑射影曲面上稳定层模空间的奇异上同调中的作用，采用相交理论方法规避了传统的$K$-理论工具。
中文摘要 AI 辅助
我们研究仿杨代数$Y_{t_1,t_2}(\boldsymbol{\text{gl}}_1)$在光滑射影曲面$S$上稳定层模空间$\boldsymbol{\text{Singular cohomology of stable sheaves}}$的奇异上同调中的作用。通过对嵌套模空间的相交理论分析，我们证明了表示$Y_{t_1,t_2}(\boldsymbol{\text{gl}}_1) \boldsymbol{\text{acts on } H_{\boldsymbol{\text{moduli space}}}}$。该相交理论方法将经典构造扩展到完整杨代数结构，规避了建立此作用通常所需的$K$-理论工具。
英文摘要
We investigate the action of the affine Yangian $Y_{t_1,t_2}(\widehat{\mathfrak{gl}}_1)$ on the singular cohomology of the moduli space of stable sheaves $\mathcal{M}$ on a smooth projective surface $S$. Through an intersection-theoretic analysis of nested moduli spaces, we obtain a proof of the representation $$Y_{t_1,t_2}(\widehat{\mathfrak{gl}}_1) \curvearrowright H_{\mathcal{M}}.$$ This intersection-theoretic approach extends classical constructions to the full Yangian structure and circumvents the $K$-theoretic machinery traditionally required to establish this action.
