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)