Geodesic
From Dimers to Tensor Invariants
Séminaire lotharingien de combinatoire, 78B (2017)

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We formulate a higher-rank version of the boundary measurement map for weighted planar bipartite networks in the disk. It sends a network to a linear combination of SLr webs, and is built upon the r-fold dimer model on the network. When r is 1, our map is a reformulation of Postnikov's boundary measurement used to coordinatize positroid strata. When r is 2 or 3, it is a reformulation of the SL2 and SL3 web immanants defined by the second author. The basic result is that the higher rank map factors through Postnikov's map. As an application, we deduce generators and relations for the space of SLr webs, reproving a result of Cautis-Kamnitzer-Morrison. We establish compatibility between our map and restriction to positroid strata, and thus between webs and total positivity. 

@article{SLC_2017_78B_a74,
     author = {Chris Fraser and Thomas Lam and Ian Le},
     title = {From {Dimers} to {Tensor} {Invariants}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a74/}
}
TY  - JOUR
AU  - Chris Fraser
AU  - Thomas Lam
AU  - Ian Le
TI  - From Dimers to Tensor Invariants
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a74/
ID  - SLC_2017_78B_a74
ER  - 
%0 Journal Article
%A Chris Fraser
%A Thomas Lam
%A Ian Le
%T From Dimers to Tensor Invariants
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a74/
%F SLC_2017_78B_a74
Chris Fraser; Thomas Lam; Ian Le. From Dimers to Tensor Invariants. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a74/