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)
Journal	Potential Analysis
DOIs	https://doi.org/10.1007/s11118-023-10084-7
State	Accepted/In press - 2023

Keywords

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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title = "Connections and Loops Intertwinning",

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 = "Holonomy, Split and merge, Yang-mills",

author = "{Le Jan}, Yves",

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

year = "2023",

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

language = "English (US)",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer Netherlands",

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T1 - Connections and Loops Intertwinning

AU - Le Jan, Yves

PY - 2023

Y1 - 2023

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.

KW - Holonomy

KW - Split and merge

KW - Yang-mills

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UR - http://www.scopus.com/inward/citedby.url?scp=85168607604&partnerID=8YFLogxK

U2 - 10.1007/s11118-023-10084-7

DO - 10.1007/s11118-023-10084-7

M3 - Article

AN - SCOPUS:85168607604

SN - 0926-2601

JO - Potential Analysis

JF - Potential Analysis

ER -

Connections and Loops Intertwinning

Abstract

Keywords

ASJC Scopus subject areas

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