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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

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    $\begingroup$ As Bruce points out, some of the answers to your previous question contained pointers to the literature. Are they insufficient, irrelevant, or unhelpful? $\endgroup$ – Yemon Choi Mar 18 '10 at 22:31
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How about:

R. E. Block, "The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra," Adv. Math. 39 (1981), 69--110. See: link text.

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  • $\begingroup$ The same link was given in Bruce's answer mathoverflow.net/questions/18559/… to the OP's previous question. It would help if he gave some indication of whether he has followed that reference and finds it useful. $\endgroup$ – Yemon Choi Mar 18 '10 at 22:30
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You have been given information and some references in your previous question.

Is there a machinery describing all the irreducible representations ?

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