论文标题
彩色$ \ mathfrak {sl} _r $ torus结的不变和$ \ mathcal的字符{w} _r $代数
Coloured $\mathfrak{sl}_r$ invariants of torus knots and characters of $\mathcal{W}_r$ algebras
论文作者
论文摘要
令$ p <p'$为一对互联网整数。在本说明中，在$ \ mathfrak {sl} _2 $的情况下概括了莫顿的作品，我们为$ \ mathfrak {sl} _r $ jons n n n n of torus nnots $ t（p，p，p，p，p，p，p'）$ color的$ \ mathfrak {sl} _r $ jones提供了一个公式。当$ r \ leq p $时，我们表明，沿$ l_r（nrλ_1）$计算的转移（非正函数，框架依赖）不变性的适当限制本质上是某些最小型模型principal principal $ \ nathcal $ \ mathcal {w} $代数的字符， $ \ MATHCAL {W} _r（P，P，P'）$，最多有些因素，独立于$ P $和$ P'$，但取决于$ r $。特别是，这些限制本质上是模块化的。我们希望这些限制是不变式序列的$ 0 $ tails。最后，我们以$ p <r $的限制制定了一个猜想。
Let $p<p'$ be a pair of coprime positive integers. In this note, generalizing Morton's work in the case of $\mathfrak{sl}_2$, we give a formula for the $\mathfrak{sl}_r$ Jones invariants of torus knots $T(p,p')$ coloured with the finite-dimensional irreducible representations $L_r(nΛ_1)$. When $r \leq p$, we show that appropriate limits of the shifted (non-normalized, framing dependent) invariants calculated along $L_r(nrΛ_1)$ are essentially the characters of certain minimal model principal $\mathcal{W}$ algebras of type $\mathrm{A}$, namely, $\mathcal{W}_r(p,p')$, up to some factors independent of $p$ and $p'$ but depending on $r$. In particular, these limits are essentially modular. We expect these limits to be the $0$-tails of corresponding sequences of invariants. At the end, we formulate a conjecture on limits for $p<r$.
