Strong 1-boundedness of unimodular orthogonal free quantum groups

Recently, Brannan and Vergnioux showed that the free orthogonal quantum group factors $\mathcal{L}\mathbb{F}O_M$ have Jung's strong 1-boundedness property, hence are not isomorphic to factors. We prove an analogous result for other unimodular case, where parameter matrix is standard symplectic in 2N dimensions $J_{2N}$. compute derivatives of defining relations by introducing self-adjoint generators through a decomposition fundamental representation terms Pauli matrices, resulting these generators. Moreover, we under certain conditions, one can add elements 1-bounded set without losing 1-boundedness. In particular this allows us include character representation, proving