I am dealing with universal C*-algebra generated by $x,y$ with the following relations: $xy = qyx$, $x^{*}y = qyx^{*}$, $y^{*}x = qxy^{*}$, $x^{*}x = q^2xx^{*} - (1-q^2)yy^{*}$, $y^{*}y = q^2yy^{*} - (1-q^2)$, where q $ \in (0,1)$. I need to find (the most simple) faithful representation of it but I couldn’t do it myself and the only reference I found is Pusz, Woronovicz “Twisted second quantization”. In this article I couldn’t understand a thing because it is written kind of with a physics notation.

Does someone by any chance know where else it is written? Or may be give me a hint how to construct it?