Generalized permutative representations of Cuntz algebras

We introduce representations of the Cuntz algebra $\text{con}$ which are parameterized by sequences in the set of unit vectors in ${\mathbf{C}}^N$. 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.