What is the relationship between representations of Lie algebra and Weyl algebra? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T14:05:35Z http://mathoverflow.net/feeds/question/18646 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/18646/what-is-the-relationship-between-representations-of-lie-algebra-and-weyl-algebra What is the relationship between representations of Lie algebra and Weyl algebra? Peter Lee 2010-03-18T19:41:12Z 2010-03-18T20:33:24Z <p>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?</p> <p>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?</p> <p>I am looking for reference</p> http://mathoverflow.net/questions/18646/what-is-the-relationship-between-representations-of-lie-algebra-and-weyl-algebra/18651#18651 Answer by Thomas Nevins for What is the relationship between representations of Lie algebra and Weyl algebra? Thomas Nevins 2010-03-18T20:33:13Z 2010-03-18T20:33:13Z <p>How about:</p> <p>R. E. Block, "The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra," Adv. Math. 39 (1981), 69--110. See: <a href="http://www.ms.unimelb.edu.au/~ram/Teaching/RepThy2008/1981AdvMathv39n1p69.pdf" rel="nofollow">link text</a>.</p> http://mathoverflow.net/questions/18646/what-is-the-relationship-between-representations-of-lie-algebra-and-weyl-algebra/18652#18652 Answer by Bruce Westbury for What is the relationship between representations of Lie algebra and Weyl algebra? Bruce Westbury 2010-03-18T20:33:24Z 2010-03-18T20:33:24Z <p>You have been given information and some references in your previous question.</p> <p><a href="http://mathoverflow.net/questions/18559/is-there-a-machinery-describing-all-the-irreducible-representations" rel="nofollow">http://mathoverflow.net/questions/18559/is-there-a-machinery-describing-all-the-irreducible-representations</a></p>