Quantum groups, q-deformed meson mass formulas and knot invariants

With quantum groups SUq(n) as n-flavor hadron symmetry groups, and with the quantum group Uq(n+1) taken to effect symmetry breakings,we obtain the q-analogs of mass sum rules (MSR's) for vector mesons that generalize well-known formulas of Gell-Mann and Okubo and multi flavor analogs. Nice agreement with data of the q-relations respectively for masses of φ, J/ψ, and γ is achieved if q=e2πi/(kn+2) where kn=8,12,16.Possible connection of these quarkonia to some knots is mentioned