Irreducible representations of simple Lie algebras by differential operators
Abstract
We describe a systematic method to construct arbitrary highestweight modules, including arbitrary finitedimensional representations, for any finite dimensional simple Lie algebra g . The Lie algebra generators are represented as first order differential operators in 1/2 (dimg rankg ) variables. All rising generators e are universal in the sense that they do not depend on representation, the weights enter (in a very simple way) only in the expressions for the lowering operators f . We present explicit formulas of this kind for the simple root generators of all classical Lie algebras.
 Publication:

European Physical Journal C
 Pub Date:
 October 2021
 DOI:
 10.1140/epjc/s10052021096767
 arXiv:
 arXiv:2106.03638
 Bibcode:
 2021EPJC...81..898M
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 Eur.Phys.J.C 81 (2021) 10, 898