论文标题
圆环链接同源性的对称函数升力
A symmetric function lift of torus link homology
论文作者
论文摘要
假设$ m $和$ n $是正整数，让$ k = \ gcd（m，n）$，$ m = m/k $，$ n = n = n/k $。我们将对称函数$ l_ {m，n} $定义为某些晶格路径的加权总和。我们表明，$ l_ {m，n} $满足了Mellit和Hogancamp的递归的概括，该递归是$ M，n $ -torus链接的三个阶层的Khovanov-Rozansky同源性。作为推论，我们获得了$ M，n $ -torus链接的三个阶级的Khovanov-Rozansky同源性，作为$ l_ {m，n} $的专业化。我们猜想$ l_ {m，n} $是等于（最高常数），椭圆形霍尔代数运算符$ \ mathbf {q} _ {m，n} $构成$ k $ times，并应用于1。
Suppose $M$ and $N$ are positive integers and let $k = \gcd(M, N)$, $m = M/k$, and $n=N/k$. We define a symmetric function $L_{M,N}$ as a weighted sum over certain tuples of lattice paths. We show that $L_{M,N}$ satisfies a generalization of Mellit and Hogancamp's recursion for the triply-graded Khovanov--Rozansky homology of the $M,N$-torus link. As a corollary, we obtain the triply-graded Khovanov--Rozansky homology of the $M,N$-torus link as a specialization of $L_{M,N}$. We conjecture that $L_{M,N}$ is equal (up to a constant) to the elliptic Hall algebra operator $\mathbf{Q}_{m,n}$ composed $k$ times and applied to 1.
