TY - JOUR

T1 - Grassmannians over rings and subpolygons

AU - Cuntz, Michael

PY - 2023/1/13

Y1 - 2023/1/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85161526471&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2207.09359

DO - 10.48550/arXiv.2207.09359

M3 - Article

VL - 2023

SP - 8078

EP - 8099

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 9

M1 - rnac350

ER -