ScalingStacks

Corollary 4.7 (Lasy). The following defines a Markov trace on finite Coxeter groups:

$${\mathcal{B}}_{(W,S)}\ni b\mapsto\sum_{d,i,j}(-1)^{j}\dim H^{j}(\operatorname{HH}\nolimits_{i}^{S}(F_{b}))_{d}q^{-d}t^{-i}\in{\mathbf{Z}}[q^{\pm 1},t^{\pm 1}]$$

corresponding to $t_{+}=-t$ and $t_{-}=1$.