Babara Lulek

Kinematics of the Heisenberg magnetic ring of N nodes, each with the spin s, has been discussed within the frame of the Weyl duality between actions of the symmetric group on N objects and the unitary group U(n) of quantum symmetry of the single-node space (n = 2s + 1), in the quantum space of the magnet. The basis of wavelets is presented, and rarefied Brillouin zones, corresponding to orbits of the translation group with non-trivial stabilizers, are pointed out. The combinatorial Robinson - Schensted - Knuth algorithm, the Jucys-Murphy operators and Kerov - Kirillov - Reshetikhin bijection are applied to partial diagonalization of the Heisenberg Hamiltonian, as well as to classification of finite analogues of string solutions.