A local normal form for Hamiltonian actions of compact semisimple Poisson–Lie groups

The main contribution of this manuscript is a local normal form for Hamiltonian actions Poisson-Lie groups $K$ on symplectic manifold equipped with an $AN$-valued moment map, where $AN$ the dual group $K$. Our proof uses delinearization theorem Alekseev which relates classical action $\mathfrak{k}^*$-valued map to via deformation structures. We obtain our result by proving ``delinearization commutes quotients'' also independent interest, and then putting together wtih maps. A key ingredient $\mathcal{D}(\omega_{can})$ canonical structure $T^*K$, so we additionally take some steps toward explicit computations $\mathcal{D}(\omega_{can})$. In particular, in case $K=SU(2)$, formulas matrix coefficients respect natural choice coordinates $T^*SU(2)$.