Iorgov M. Representations of quantum algebras of physical symmetries and their application for treatment of hadron masses

In the thesis, representations of q-deformed analogs U'q(so(n)), Uq(iso(n)) and Uq(u(n,1)) of Lie algebras of rotation, Euclidean and pseudounitary groups are explored, along with their applications.For the algebras U'q(so(n)), Uq(iso(n)) (n>5), a theorem on irreducible representations (in Gel'fand--Tsetlin basis) is proved. Basis Casimir elements for the algebra U'q(so(n)), n=4,5,6, are found. Quantum algebras Uq(u(n)) and Uq(u(n,1)) are used to derive new mass relations (more accurate than the Gell-Mann--Okubo one) for baryons 1/2+.It is shown, that usage of quantum algebras as describing flavorsymmetries of hadrons accounts for nonlinear contributions in SU(3)-breaking. Within anyonic realization of Uq(su(n)), the state vectors for mesons 1- and baryons 3/2+ are constructed, and mass sum rules obtained.