Connections and Loops Intertwinning

Yves Le Jan

Research output: Contribution to journalArticlepeer-review


On a finite graph, we prove that trace of holonomies determine an intertwining relation between merge-and-split generators on collections of geodesic loops ensembles and Casimir operators on moduli of unitary connections. By adding a deformation part to the generator on loops, this result is extended to the Casimir operator modified in order to be self adjoint with respect to Yang-Mills measure.

Original languageEnglish (US)
Pages (from-to)1215-1229
Number of pages15
JournalPotential Analysis
Issue number3
StatePublished - Mar 2024


  • 60G60
  • 60J27
  • Holonomy
  • Split and merge
  • Yang-mills

ASJC Scopus subject areas

  • Analysis


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