Continuous Hecke algebras

The theory of PBW properties of quadratic algebras, to which this paper aims to be a modest contribution, originates from the pioneering work of Drinfeld (see [Dr1]). In particular, as we learned after publication of [EG] (to the embarrassment of two of us!), symplectic reflection algebras, as well as PBW theorems for them, were discovered by Drinfeld in the classical paper [Dr2] 15 years before [EG] (namely, they are a special case of degenerate affine Hecke algebras for a finite group G introduced in [Dr2, Section 4]).