The literature has definitions (seemingly plural, though they might be linked) of a $q$-deformed Virasoro algebra. But is there any link of these to a $q$-deformed Heisenberg algebra? (Classically there is an expression for $L\_n$ in terms of a normal ordered quadratic in the generators of the Heisenberg algebra.) I would be grateful for a reference to somewhere that discusses this in terms understandable to a non-expert in conformal field theory. However anything to shed light on the current status of the q-Virasoro and q-Heisenberg algebras, or relates them to the undeformed theory, would be of interest.


Apologies for my ignorance on this subject, as I pointed out I am certainly not an expert in CFT. I am currently trying to sort this out as an example of the action of vector fields in noncommutative geometry...



q-Virasoro and q-Heisenberg algebras
The main sources are Awata et al or Frenkel-Reshetikhin. In <http://arxiv.org/pdf/q-alg/9507034v5.pdf> section 4, you can see the q,t case. You can also look at <http://arxiv.org/pdf/q-alg/9505025v1.pdf> where the introduction gives more references to how this relates to the undeformed case. This gives the classical Virasoro as functions on opers on the punctured disc.


