https://doi.org/10.1140/epjc/s10052-021-09676-7
Letter
Irreducible representations of simple Lie algebras by differential operators
1
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
Received:
16
June
2021
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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