From dimers to tensor invariants

Chris Fraser, Thomas Lam, Ian Le

Research output: Contribution to conferencePaperpeer-review

Abstract

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 SLrwebs, 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 co-ordinatize positroid strata. When r is 2 or 3, it is a reformulation of the SL2and SL3web 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 SLrwebs, 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.

Original languageEnglish (US)
StatePublished - 2006
Externally publishedYes
Event29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom
Duration: Jul 9 2017Jul 13 2017

Conference

Conference29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017
CountryUnited Kingdom
CityLondon
Period7/9/177/13/17

Keywords

  • Boundary measurement
  • Dimer
  • Grassmannian
  • Positroid
  • Web

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'From dimers to tensor invariants'. Together they form a unique fingerprint.

Cite this