ub.xmlui.mirage2.page-structure.muninLogoub.xmlui.mirage2.page-structure.openResearchArchiveLogo
    • EnglishEnglish
    • norsknorsk
  • Velg spraakEnglish 
    • EnglishEnglish
    • norsknorsk
  • Administration/UB
View Item 
  •   Home
  • Fakultet for naturvitenskap og teknologi
  • Institutt for matematikk og statistikk
  • Artikler, rapporter og annet (matematikk og statistikk)
  • View Item
  •   Home
  • Fakultet for naturvitenskap og teknologi
  • Institutt for matematikk og statistikk
  • Artikler, rapporter og annet (matematikk og statistikk)
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Orbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description

Permanent link
https://hdl.handle.net/10037/34443
DOI
https://doi.org/10.1137/23M158173X
Thumbnail
View/Open
article.pdf (2.172Mb)
Accepted manuscript version (PDF)
Date
2024
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Author
Hubert, Evelyne; Metzlaff, Tobias; Riener, Cordian Benedikt
Abstract
The 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.
Publisher
Society for Industrial and Applied Mathematics
Citation
Hubert, Metzlaff, Riener. Orbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description. SIAM Journal on applied algebra and geometry. 2024
Metadata
Show full item record
Collections
  • Artikler, rapporter og annet (matematikk og statistikk) [354]
Copyright 2024 The Author(s)

Browse

Browse all of MuninCommunities & CollectionsAuthor listTitlesBy Issue DateBrowse this CollectionAuthor listTitlesBy Issue Date
Login

Statistics

View Usage Statistics
UiT

Munin is powered by DSpace

UiT The Arctic University of Norway
The University Library
uit.no/ub - munin@ub.uit.no

Accessibility statement (Norwegian only)