Wave functions of multiquark hadrons from representations of the symmetry groups Sn

Construction of the wave functions of multiquark hadrons by a traditional method based on the tensor products of colors, flavors, spins (and orbital) parts becomes quite complex when quark numbers grow n=5,6..12, as it gets difficult to satisfy the requirements of Fermi statistics. Our novel approach is focused directly on representations of the permutation symmetry generators. After showing how C3 is manifested in the wave functions of (excited) baryons, we use it to construct the wave functions for a set of pentaquarks and hexaquarks (n=5,6). We also have some partial results for larger systems, with n=9 and 12, and even beyond that as far as n=24.