q-dimensional formulas for the cyclic polyene Hubbard model

Abstract

Through rather tedious algebraic manipulations involving ratios of polynomials with fractional powers the generating polynomials result from q-dimensional formulas. U (n) down arrow O (m,m) down arrow C-n branching rules are given to account firstly for the Quasi-Spin invariance (U (n) down arrow O (m,m)) and then the Spatial Symmetry invariance (O (m, m) down arrow C-n) due to C-n. The resulting expressions may be efficiently handled using the symbolic computation language MAPLE and the dimensional information for an arbitrary spin, isospin and quasimomentum obtained.