I need to determine the adjoint operator to $a_i$:
$a_i |n_0, n_1, ... \rangle_S = \sqrt{n_i} |n_0, n_1, ..., n_{i-1}, n_i - 1, n_{i+1}, .. \rangle_S$
where the $S$ should denote the symmetrizer. I just don't know how to determine the adjoint, we have done this only for "simple" operators.
• So you mean taking the $a^T$? – Darius Jan 11 '16 at 9:37