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 -