Quantum isometry group of dual of finitely generated discrete groups- $\textrm{II}$

As a contribution of the programme of Goswami and Mandal (2014), we carry out explicit computations of $\mathbb{Q}(Γ,S)$, the quantum isometry group of the canonical spectral triple on $C_{r}^{*}(Γ)$ coming from the word length function corresponding to a finite generating set S, for several interesting examples of $Γ$ not covered by the previous work Goswami and Mandal (2014). These include the braid group of 3 generators, $\mathbb{Z}_4^{*n}$ etc. Moreover, we give an alternative description of the quantum groups $H_s^{+}(n,0)$ and $K_n^{+}$ (studied in Banica and Skalski (2012), Banica and Skalski (2013)) in terms of free wreath product. In the last section we give several new examples of groups for which $\mathbb{Q}(Γ)$ turn out to be doubling of $C^*(Γ)$.

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