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

Band

2023

Seiten

8078-8099

Anzahl der Seiten

22

ISSN

1073-7928

Publikationsdatum

13.01.2023

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.)

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2207.09359 (Zugang: Offen)
https://doi.org/10.1093/imrn/rnac350 (Zugang: Geschlossen)