rt.representation theory - What is the relationship between representations of Lie algebra and Weyl algebra?

Is there any paper talking about the relationship of representation of finite dimensional Lie algebra and Weyl algebra? Can we construct representations of Lie algebra from representations of Weyl algebra?

There is a notion of quantized Weyl algebra. Is there a explicit relation between representation of quantized Weyl algebra and representation of quantized enveloping algebra?

I am looking for reference