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Publikationsdetails

Publikationsdetails

Grassmannians over rings and subpolygons

verfasst von
Michael Cuntz
Abstract

We investigate special points on the Grassmannian which correspond to friezes with coefficients in the case of rank two. Using representations of arithmetic matroids we obtain a theorem on subpolygons of specializations of the coordinate ring. As a special case we recover the characterization of subpolygons in classic frieze patterns. Moreover, we observe that specializing clusters of the coordinate ring of the Grassmannian to units yields representations that may be interpreted as arrangements of hyperplanes with notable properties. In particular, we get an interpretation of certain Weyl groups and groupoids as generalized frieze patterns.

Organisationseinheit(en)
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Typ
Artikel
Journal
International Mathematics Research Notices
ISSN
1073-7928
Publikationsdatum
13.01.2023
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
Elektronische Version(en)
https://doi.org/10.48550/arXiv.2207.09359 (Zugang: Offen)
https://doi.org/10.1093/imrn/rnac350 (Zugang: Geschlossen)