  We investigate the two-sided symmetric extendibility problem of Werner
states. The interplay of the unitary symmetry of these states and the inherent
bipartite permutation symmetry of the extendibility scenario allows us to map
this problem into the ground state problem of a highly symmetric spin-model
Hamiltonian. We solve this ground state problem analytically by utilizing the
representation theory of SU(d), in particular a result related to the dominance
order of Young diagrams in Littlewood-Richarson decompositions. As a result, we
obtain necessary and sufficient conditions for the extendibility of Werner
states for arbitrary extension size and local dimension. Interestingly, the
range of extendible states has a non-trivial trade-off between the extension
sizes on the two sides. We compare our result with the two-sided extendibility
problem of isotropic states, where there is no such trade-off.
