Around the center
Representation Theory
2025-10-07 v1
Abstract
The center of a semisimple Lie algebra can be described as the algebra of W-invariant functions on the dual of the Cartan subalgebra. The centers of many Lie superalgebras have a similar description, but the defining equivalence relation on the dual of the Cartan subalgebra is not given by a finite group action. Lagrangian equivalence relations that we introduce generalize the action of a subgroup of the orthogonal group. Using them, we present a new proof of a result by Ian Musson about the centers of Lie superalgebras. Our proof is not based on a case-by-case analysis.
Cite
@article{arxiv.2510.03928,
title = {Around the center},
author = {Maria Gorelik and Vladimir Hinich and Vera Serganova},
journal= {arXiv preprint arXiv:2510.03928},
year = {2025}
}
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19 pages