Communications in Number Theory and Physics

Volume 4 (2010)

Number 1

Hecke correspondences and Feynman graphs

Pages: 161 – 185

DOI: http://dx.doi.org/10.4310/CNTP.2010.v4.n1.a4

Author

Matt Szczesny (Department of Mathematics, Boston University, Boston, Mass., U.S.A.)

Abstract

We consider natural representations of the Connes–KreimerLie algebras on rooted trees/Feynman graphs arising fromHeckecorrespondences in the categories $\LRF, \LFG$constructed by K. Kremnizer and the author. We thus obtainthe insertion/elimination representations constructed byConnes–Kreimer as well as an isomorphic pair that we termtop-insertion/top-elimination. We also construct gradedfinite-dimensional sub/quotient representations of thesearising from “truncated” correspondences.

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