Operator techniques in the Hopf algebra for a symmetric group within Racah calculus for Bethe Ansatz eigenfunctions

摘要

We propose some operator techniques, applicable in the proce-dure of an immediate diagonalization for the Heisenberg chain,such as projection operators for subspaces with definite quasi-momentum, total or partial spin, quasimomenta of strings etc.These techniques yield, in particular, matrices of appropriate Clebsch- Gordan coefficients, and reduce significantly the sizeof an effective Hamiltonian matrix. We apply the basis ofwavelets to exploit the translational symmetry, along theSchwinger scheme of unitary geometry, applied to a single N-dimensional magnon space.