Hermitian quantum generator convention ($H_X=i\rho (X)$)

For a unitary derived representation $\rho$, its generators are anti-Hermitian. Define Hermitian observables $H_X=i\rho (X)$; then their ordinary operator commutator is $[H_X,H_Y]=i{H}_{[X,Y]}$. Thus real Lie algebra structure constants and Hermitian-operator commutation relations differ by an $i$. Products in a universal enveloping algebra require one conversion factor for every generator. In particular, the abstract bilinear Pauli-Lubanski element has representation image minus the pseudovector formed from the Hermitian physical generators.