A class of representations of $C^{\ast }$-algebra generated by $q_{ij}$-commuting isometries

For $C^{\ast }$-algebra generated by a finite family of isometries $s_j$, $j=1,\dots ,d$ satisfying $q_{ij}$-commutation relations $$s_j^{\ast }{s}_j=I,s_j^{\ast }{s}_k=q_{ij}{s}_k{s}_j^{\ast },q_{ij}={\bar{q}}_{ji},\mathrm{\mid }{q}_{ij}\mathrm{\mid }<1,1\le i\mathrm{\ne }j\le d,$$ we construct an infinite family of unitarily non-equivalent irreducible representations. These representations are deformations of the corresponding class of representations of the Cuntz algebra ${\mathcal{O}}_d$.