Publication details

Grassmannians over rings and subpolygons

authored by
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.

Organisation(s)
Institute of Algebra, Number Theory and Discrete Mathematics
Type
Article
Journal
International Mathematics Research Notices
Volume
2023
Pages
8078-8099
No. of pages
22
ISSN
1073-7928
Publication date
13.01.2023
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Mathematics(all)
Electronic version(s)
https://doi.org/10.48550/arXiv.2207.09359 (Access: Open)
https://doi.org/10.1093/imrn/rnac350 (Access: Closed)