论文标题
$ P = W $通过$ \ Mathcal {H} _2 $
$P=W$ via $\mathcal{H}_2$
论文作者
论文摘要
令$ \ MATHCAL {H} _2 $为符号平面上多项式Hamiltonian矢量字段的Lie代数。令$ x $为固定相对优质等级和学位的稳定希格斯捆绑的模量空间，或更一般而言，稳定的抛物线寄生抛物线Higgs的模量空间是任意等级和学位的通用稳定性条件的模量。令$ h^*（x）$为具有理性系数的同胞。使用重言式类和Hecke通信的杯形产品的操作，我们在$ h^*（x）[x，y] $上构建了$ \ Mathcal {h} _2 $的动作，其中$ x $和$ y $是正式变量。我们表明，$ h^*（x）上的不正当过滤与过滤与$ \ mathfrak {sl} _2 \ subset \ subset \ mathcal {h} _2 $相关，并推断出$ p = w $ de cataldo-hausel-hausel-hausel-migliorini。
Let $\mathcal{H}_2$ be the Lie algebra of polynomial Hamiltonian vector fields on the symplectic plane. Let $X$ be the moduli space of stable Higgs bundles of fixed relatively prime rank and degree, or more generally the moduli space of stable parabolic Higgs bundles of arbitrary rank and degree for a generic stability condition. Let $H^*(X)$ be the cohomology with rational coefficients. Using the operations of cup-product by tautological classes and Hecke correspondences we construct an action of $\mathcal{H}_2$ on $H^*(X)[x,y]$, where $x$ and $y$ are formal variables. We show that the perverse filtration on $H^*(X)$ coincides with the filtration canonically associated to $\mathfrak{sl}_2\subset \mathcal{H}_2$ and deduce the $P=W$ conjecture of de Cataldo-Hausel-Migliorini.
