Separating monomials for diagonalizable actions

Domokos, M.

doi:10.1112/blms.12722

Bulletin of London Math Soc

2022

DOI: 10.1112/blms.12722

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Separating monomials for diagonalizable actions

M. Domokos

Abstract: Sets of monomials separating Zariski closed orbits under diagonalizable group actions are characterized in terms of the corresponding monoid of product-one sequences over the character group. This is applied to compare the degree bounds for separating invariants and generating invariants of diagonalizable group actions.

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2024

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Cited by 3 publications

References 28 publications

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Group-Invariant Max Filtering

Cahill,

Iverson,

Mixon

et al. 2024

Found Comput Math

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Given a real inner product space V and a group G of linear isometries, we construct a family of G-invariant real-valued functions on V that we call max filters. In the case where $$V={\mathbb {R}}^d$$ V = R d and G is finite, a suitable max filter bank separates orbits, and is even bilipschitz in the quotient metric. In the case where $$V=L^2({\mathbb {R}}^d)$$ V = L 2 ( R d ) and G is the group of translation operators, a max filter exhibits stability to diffeomorphic distortion like that of the scattering transform introduced by Mallat. We establish that max filters are well suited for various classification tasks, both in theory and in practice.

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Group-Invariant Max Filtering

Cahill,

Iverson,

Mixon

et al. 2024

Found Comput Math

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show abstract

Towards a bilipschitz invariant theory

Cahill,

Iverson,

Mixon

2024

Applied and Computational Harmonic Analysis

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Degree bounds for fields of rational invariants of Z/pZ and other finite groups

Blum-Smith,

Garcia,

Hidalgo

et al. 2024

Journal of Pure and Applied Algebra

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Separating monomials for diagonalizable actions

Cited by 3 publications

References 28 publications

Group-Invariant Max Filtering

Group-Invariant Max Filtering

Towards a bilipschitz invariant theory

Degree bounds for fields of rational invariants of Z/pZ and other finite groups

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