MATRIX REPRESENTATION OF HIGHER INTEGER CONFORMAL SPIN SYMMETRIES

Using infinite matrices, we construct the generating functional of hig her integer conformal spin extensions of the Virasoro algebra and the SU(2) spin 1/2 representation loop algebra. Higher conformal spin symm etries are realized on the set F-1/2 of the configurations of the homo geneous Ising chain. This is an infinite-dimensional vector space redu cible into subspaces F-1/2(m)(l), m is an element of Z, l is an elemen t of N, completely specified by the site occupation operator number an d the degree of the excitations of the chain states. The algebra of th e chain transformations is given by the central extension of the algeb ra of the site state ones. The anomalous term of the generating functi onal of the higher integer conformal spin extensions of the Virasoro a lgebra is calculated and a comment on the unitarity is made. Other pro perties are discussed. (C) 1995 American Institute of Physics.