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dc.contributor.authorHubert, Evelyne
dc.contributor.authorMetzlaff, Tobias
dc.contributor.authorRiener, Cordian Benedikt
dc.date.accessioned2024-08-27T12:27:50Z
dc.date.available2024-08-27T12:27:50Z
dc.date.issued2024
dc.description.abstractThe Weyl group of a crystallographic root system has a multiplicative action on the compact torus. The orbit space of this action is a compact basic semi-algebraic set. We present a polynomial description of this set for the Weyl groups associated to root systems of types A, B, C, D and G. Our description is given through a polynomial matrix inequality. The novelty lies in an approach via Hermite quadratic forms and a closed form formula for the matrix entries. The orbit space of the multiplicative Weyl group action is the orthogonality region of generalized Chebyshev polynomials. In this polynomial basis, we show that the matrices obtained for the five types follow the same, surprisingly simple pattern. This is applied to the optimization of trigonometric polynomials with crystallographic symmetries.en_US
dc.identifier.citationHubert, Metzlaff, Riener. Orbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description. SIAM Journal on applied algebra and geometry. 2024en_US
dc.identifier.cristinIDFRIDAID 2287635
dc.identifier.doi10.1137/23M158173X
dc.identifier.issn2470-6566
dc.identifier.urihttps://hdl.handle.net/10037/34443
dc.language.isoengen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.journalSIAM Journal on applied algebra and geometry
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2024 The Author(s)en_US
dc.titleOrbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Descriptionen_US
dc.type.versionacceptedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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