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

Shashank Kanade

We study coloured invariants of torus knots $T(p,p^{\prime })$ (where $p,p^{\prime }$ are coprime positive integers). When the colouring Lie algebra is simply-laced, and when $p,p^{\prime }\ge h^{\vee }$, we u…