Masses of Decuplet Baryons Treated within Anyonic Realization of the q-Algebras U_q(su_N)

In the approach to hadronic flavour symmetries based on the q-algebras U_q(su_N) and proved to be realistic, the known construction of U_q(su_N) in terms of anyonic oscillators residing on 2d lattice is utilized. Anyonic Fock-like realization of basis state vectors is given for baryons (3/2)^+ from the 10-plet of U_q(su_3) embedded, via 20-plet of U_q(su_4), into the “dynamical” representation [4000] of U_q(su_5). Within the anyonic picture, we reobtain the universal q-deformed decuplet mass relation M_\Omega-M_{\Xi^}+M_{\Sigma^}-M_{\Delta}=[2]q (M{\Xi^}-M_{\Sigma^}), where [2]_q=q+q^{-1}=2 cos{\theta}. Consistency with data for baryon masses requires \theta\simeq\frac{\pi}{14}. As a result, anyons with anyonic statistics parameter \nu = 1/14 can be put into correspondence, at least formally, with the constituent quarks of decuplet baryons.