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Pré-Publication, Document De Travail Année : 2022

Polynomial description for the T-Orbit Spaces of Multiplicative Actions

Résumé

A finite group with an integer representation has a multiplicative action on the ring of Laurent polynomials, which is induced by a nonlinear action on the complex torus. We study the structure of the associated orbit space as the image of the fundamental invariants. For the Weyl groups of types A, B, C and D, this image is a compact basic semi-algebraic set and we present the defining polynomial inequalities explicitly. We show how orbits correspond to solutions in the complex torus of symmetric polynomial systems and give a characterization of the orbit space as the positivity-locus of a symmetric real matrix polynomial. The resulting domain is the region of orthogonality for a family of generalized Chebyshev polynomials, which have connections to topics such as Fourier analysis and representations of Lie algebras.
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Dates et versions

hal-03590007 , version 1 (26-02-2022)
hal-03590007 , version 2 (11-05-2022)
hal-03590007 , version 3 (26-06-2023)
hal-03590007 , version 4 (26-02-2024)

Identifiants

  • HAL Id : hal-03590007 , version 2

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Evelyne Hubert, Tobias Metzlaff, Cordian Riener. Polynomial description for the T-Orbit Spaces of Multiplicative Actions. 2022. ⟨hal-03590007v2⟩
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