Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras

Alessandro Torrielli; Sanjaye Ramgoolam; Sebastian De Haro

Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras

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arxiv hep-th/0603056 v2 pith:5SR4EXWG submitted 2006-03-07 hep-th math.QA

Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras

Sebastian de Haro , Sanjaye Ramgoolam , Alessandro Torrielli This is my paper

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keywords algebrasexpansiongroupsdualityfunctionsheckelargeq-deformed

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We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality of quantum groups. The appearance of Euler characters of configuration spaces of Riemann surfaces in the expansion persists. We discuss the geometrical meaning of these formulae.

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