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Generating Functions for Casimir Invariants of Simple Lie Algebras
Abstract
We consider generalised Casimir operators associated with irreducible representations for finite-dimensional, semisimple, complex Lie algebras. Using Klimyk's formula and Okubo's formula, we derive a rational ordinary generating function for the Casimir operator eigenvalues for simple Lie algebras which does not rely on knowledge of the Weyl group. We also directly reproduce generating function expressions for the classical Lie algebras originally due to Perelomov and Popov.
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BibTeX
@misc{flattery2026generating,
title = {{Generating Functions for Casimir Invariants of Simple Lie Algebras}},
author = {Michael Flattery and Michael P. Tuite},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30635},
eprint = {2609.30635},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30635},
}
RIS
TY - UNPB
TI - Generating Functions for Casimir Invariants of Simple Lie Algebras
AU - Michael Flattery
AU - Michael P. Tuite
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30635
UR - https://arxiv.org/abs/2609.30635
AB - We consider generalised Casimir operators associated with irreducible representations for finite-dimensional, semisimple, complex Lie algebras. Using Klimyk's formula and Okubo's formula, we derive a rational ordinary generating function for the Casimir operator eigenvalues for simple Lie algebras which does not rely on knowledge of the Weyl group. We also directly reproduce generating function expressions for the classical Lie algebras originally due to Perelomov and Popov.
ER -