Matrix representation of higher integer conformal spin symmetries
Copyright policy )Matrix representation of higher integer conformal spin symmetries
Using infinite matrices, we construct the generating functional of higher integer conformal spin extensions of the Virasoro algebra and the SU(2) spin 1/2 representation loop algebra. Higher conformal spin symmetries are realized on the set F1/2 of the configurations of the homogeneous Ising chain. This is an infinite-dimensional vector space reducible into subspaces Fm1/2(l), m∈Z, l∈N, completely specified by the site occupation operator number and the degree of the excitations of the chain states. The algebra of the chain transformations is given by the central extension of the algebra of the site state ones. The anomalous term of the generating functional of the higher integer conformal spin extensions of the Virasoro algebra is calculated and a comment on the unitarity is made. Other properties are discussed.
higher integer conformal spin extension, Virasoro algebra, Virasoro and related algebras, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, loop algebra, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, homogeneous Ising chain
higher integer conformal spin extension, Virasoro algebra, Virasoro and related algebras, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, loop algebra, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, homogeneous Ising chain
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