对数顶点算子代数的特征标与环面链环的着色不变量

环面结的着色不变量、$\mathcal{W}$ 代数与相对渐近权重重数

Coloured invariants of torus knots, $\mathcal{W}$ algebras, and relative asymptotic weight multiplicities

本文利用主仿射 $\mathcal{W}$ 代数表示论研究 simply-laced 李代数着色环面结不变量的尾随单项式，证明重整化不变量的极限等于相应 $\mathcal{W}$ 代数模的特征标，并基于渐近权重重数猜想在若干例子中加以验证。

Coloured $\mathfrak{sl}_r$ invariants of torus knots and characters of $\mathcal{W}_r$ algebras

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 independ…

On the Analytic Properties of the z-Coloured Jones Polynomial

We analyse the possibility of defining complex valued Knot invariants associated with infinite dimensional unitary representations of $SL(2,R)$ and the Lorentz Group taking as starting point the Kontsevich Integral and the notion of infinitesimal character. This yields a family of knot invariants whose target space is the set of formal power series in $C$, which contained in the Melvin-Morton expansion of the coloured Jones polynomial. We verify that for some knots the series have zero radius of convergence and analyse the construction of functions of which this series are asymptotic expansion…

On Logarithmic Sobolev Inequality for the Noncommutative Two Torus

An analogue of Gross' logarithmic Sobolev inequality for a class of elements of noncommutative two tori is proved.

环面链 $T_{2s,2t}$ 与 $(s,t)$-对数 VOA

Torus links $T_{2s,2t}$ and $(s,t)$-log VOA

本文建立环面链 $T_{2s,2t}$ 与对数 $(s,t)$ VOA 的联系，证明其单线态特征等同于 Kashaev 不变量并具量子模性，且可由 $N$ 着色 Jones 多项式尾项得到，同时给出几何计算方法。

Radford, Drinfeld, and Cardy boundary states in (1,p) logarithmic conformal field models

We introduce p-1 pseudocharacters in the space of (1,p) model vacuum torus amplitudes to complete the distinguished basis in the 2p-dimensional fusion algebra to a basis in the whole (3p-1)-dimensional space of torus amplitudes, and the structure constants in this basis are integer numbers. We obtain a generalized Verlinde-formula that gives these structure constants. In the context of theories with boundaries, we identify the space of vacuum torus amplitudes with the space of Ishibashi states. Then, we propose 3p-1 boundary states satisfying the Cardy condition.