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The universal Lie algebra associatedto a root system I

✍ Scribed by Amédée Debiard; Bernard Gaveau

Publisher
Elsevier Science
Year
2000
Tongue
French
Weight
200 KB
Volume
124
Category
Article
ISSN
0007-4497

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✦ Synopsis

To any classical root system, one can associate a universal infinite dimensional Lie algebra of second order differential operators. In this work, we study this Lie algebra for rank 3 root system and show that it is semi simple, we show that it is related to the Eulerian polynomials.

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We present an algorithm for the computation of representations of a Lie algebra acting on its universal enveloping algebra. This is a new algorithm which permits the effective computation of these representations and of the matrix elements of the corresponding Lie group. The approach is based on a m