2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101255We introduce representations of the Cuntz algebra $\con$ which are parameterized by sequences in the set of unit vectors in ${\bf C}^{N}$. These representations are natural generalizations of permutative representations by Bratteli-Jorgensen and Davidson-Pitts. We show their existence, irreducibility, equivalence, uniqueness of irreducible decomposition and decomposition formulae by using parameters of representations.19 pagesOperator AlgebrasRepresentation Theory47D25text