Connections and Loops Intertwinning

Yves Le Jan

doi:10.1007/s11118-023-10084-7

Connections and Loops Intertwinning

Yves Le Jan

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	1215-1229
Number of pages	15
Journal	Potential Analysis
Volume	60
Issue number	3
DOIs	https://doi.org/10.1007/s11118-023-10084-7
State	Published - Mar 2024

Keywords

60G60
60J27
Holonomy
Split and merge
Yang-mills

ASJC Scopus subject areas

Analysis

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10.1007/s11118-023-10084-7

Cite this

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abstract = "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.",

keywords = "60G60, 60J27, Holonomy, Split and merge, Yang-mills",

author = "{Le Jan}, Yves",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature B.V. 2023.",

year = "2024",

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doi = "10.1007/s11118-023-10084-7",

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N2 - 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.

AB - 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.

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KW - Holonomy

KW - Split and merge

KW - Yang-mills

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Connections and Loops Intertwinning

Abstract

Keywords

ASJC Scopus subject areas

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