Polynomiality for algebras of invariants associated with some Inönü-Wigner contractions in type A
Abstract
This paper deals with polynomiality of algebras of symmetric invariants (or generated by symmetric semi-invariants) associated with some particular Inönü-Wigner contractions in type A. More precisely we are interested with contractions of some parabolic subalgebras in type A with respect to their decomposition into their Levi factor and their nilpotent radical, the latter becoming an abelian ideal of the contraction. When the parabolic subalgebra p has its Levi factor decomposing into three blocks, which are symmetric with respect to the antidiagonal, we show in this article that the algebra of symmetric invariants associated with the contraction of the canonical truncation of p has a Weistrass section. It follows that such an algebra of invariants is a polynomial algebra, for which we can give the number of algebraically independent homogeneous generators, their weight and degree. The method relies on the construction of an adapted pair for such a contraction. When the Levi factor of p has its central block not of the same size as its two extremal blocks, we also show that the above algebra of symmetric invariants is equal to the algebra generated by symmetric semi-invariants associated with the Inönü-Wigner contraction of p.
Related
- Generating Functions for Casimir Invariants of Simple Lie Algebras
- Additive invariants of Finite-dimensional DG-algebras
- Invariants of Nilpotent Lie Algebras via Geometry and Algebra with a Focus on Computation
- Gauge invariants raised from commutators of unimodular Hopf algebras
- ASSOCIATED PRIMES, WITNESSES, AND OMEGA INVARIANTS OF MONOMIAL IDEALS
BibTeX
@misc{fauquantmillet2026polynomiality,
title = {{Polynomiality for algebras of invariants associated with some Inönü-Wigner contractions in type A}},
author = {Florence Fauquant-Millet},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.01173},
eprint = {2609.01173},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01173},
}
RIS
TY - UNPB
TI - Polynomiality for algebras of invariants associated with some Inönü-Wigner contractions in type A
AU - Florence Fauquant-Millet
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.01173
UR - https://arxiv.org/abs/2609.01173
AB - This paper deals with polynomiality of algebras of symmetric invariants (or generated by symmetric semi-invariants) associated with some particular Inönü-Wigner contractions in type A. More precisely we are interested with contractions of some parabolic subalgebras in type A with respect to their decomposition into their Levi factor and their nilpotent radical, the latter becoming an abelian ideal of the contraction. When the parabolic subalgebra p has its Levi factor decomposing into three blocks, which are symmetric with respect to the antidiagonal, we show in this article that the algebra of symmetric invariants associated with the contraction of the canonical truncation of p has a Weistrass section. It follows that such an algebra of invariants is a polynomial algebra, for which we can give the number of algebraically independent homogeneous generators, their weight and degree. The method relies on the construction of an adapted pair for such a contraction. When the Levi factor of p has its central block not of the same size as its two extremal blocks, we also show that the above algebra of symmetric invariants is equal to the algebra generated by symmetric semi-invariants associated with the Inönü-Wigner contraction of p.
ER -