Communications in Mathematical Physics

, Volume 273, Issue 2, pp 317–355 | Cite as

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

  • Sebastian de Haro
  • Sanjaye Ramgoolam
  • Alessandro Torrielli


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.


Partition Function Modulus Space Riemann Surface Wilson Loop Conjugacy Class 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Sebastian de Haro
    • 1
  • Sanjaye Ramgoolam
    • 2
  • Alessandro Torrielli
    • 3
  1. 1.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutGolmGermany
  2. 2.Department of Physics, Queen MaryUniversity of LondonLondonUK
  3. 3.Institut für PhysikHumboldt Universität zu BerlinBerlinGermany

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