Irreducible representations of simple Lie algebras by differential operators
ITEP, 117218, Moscow, Russia
2 IITP, 127994, Moscow, Russia
3 MIPT, 141701, Dolgoprudny, Russia
4 ITMP, 119991, Moscow, Russia
5 SISSA, Trieste, Italy
6 INFN, Sezione di Trieste, Trieste, Italy
7 IGAP, Trieste, Italy
Accepted: 20 September 2021
Published online: 12 October 2021
We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra . The Lie algebra generators are represented as first order differential operators in variables. All rising generators 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 . We present explicit formulas of this kind for the simple root generators of all classical Lie algebras.
© The Author(s) 2021
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