ScalingStacks

Remark 3.2.6. Define a filtration on ${\mathbf{F}}_{2}[\hat{{\mathfrak{S}}}_{n}]$ with $({\mathbf{F}}_{2}[\hat{{\mathfrak{S}}}_{n}])^{\geq-i}$ the subspace spanned by group elements $w\in\hat{{\mathfrak{S}}}_{n}$ with $\ell(w)\leq i$. The associated graded algebra is $\hat{H}_{n}$.