states can be combined into basis states of two ${\rm sp}(2, {{\mathbb{R}}})$ irreps, characterized by $\tau - \frac{1}{2}$ and $\tau + \frac{1}{2}$, respectively. The latter can be written as $$\begin{split}
  & |\tau - \tfrac{1}{2}, \tau + N - \tfrac{1}{2}, q + \tfrac{1}{2}\rangle = \alpha_N |-, \tau + N - \tfrac{1}{2}, 
        q + \tfrac{1}{2}\rangle + \beta_N |+, \tau + N - \tfrac{1}{2}, q + \tfrac{1}{2}\rangle, \\
  & |\tau + \tfrac{1}{2}, \tau + N + \tfrac{1}{2}, q + \tfrac{1}{2}\rangle = \gamma_N |-, \tau + N + \tfrac{1}{2}, 
        q + \tfrac{1}{2}\rangle + \delta_N |+, \tau + N + \tfrac{1}{2}, q + \tfrac{1}{2}\rangle,
\end{split}$$ with $$\begin{split}
  & \alpha_N = \left(\frac{[N + (2n+a+b)k](N + nk)}{n (2n+a+b)k^2}\right)^{1/2}, \\ 
  & \beta_N = - \left(\frac{N[N + (n+a+b)k]}{n (2n+a+b)k^2}\right)^{1/2}, \\
  & \gamma_N = \left(\frac{(N + 1)(N + nk + 1)}{(n+a+b) (2n+a+b)k^2}\right)^{1/2}, \\ 
  & \delta_N = - \left(\frac{[N + (n+a+b)k + 1][N + (2n+a+b)k + 1]}{(n+a+b)(2n+a+b)k^2}\right)^{1/2}.        
\end{split}$$ On the other hand, the two-fermion states belong to a single ${\rm sp}(2, {{\mathbb{R}}})$ LWS irrep specified by $\tau$: $$|\tau, \tau + N, q + 1\rangle = |\pm, \tau + N, q + 1\rangle.$$ Hence, for any $n \ne 0$ there exists an ${\rm osp}(2/2, {{\mathbb{R}}})$ irrep, which is not a LWS one 