We discuss some aspects of the deformed W-algebras W_{ q,t}[g]. In particular, we derive an explicit formula for the Kac determinant, and discuss the center when t^2 is a primitive k-th root of unity. The relation of the structure of W_{ q,t}[g] to the representation ring of the quantum affine algebra U_q(\hat g), as discovered recently by Frenkel and Reshetikhin, is further elucidated in some examples.
Categories: math.QA hep-th