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

de Haro, Sebastian; Ramgoolam, Sanjaye; Torrielli, Alessandro

doi:10.1007/s00220-007-0232-4

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

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de Haro, Sebastian
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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cmp273_317.pdf
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0603056v2.pdf
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Citation

de Haro, S., Ramgoolam, S., & Torrielli, A. (2007). Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras. Communications in Mathematical Physics, 273(2), 317-355. doi:10.1007/s00220-007-0232-4.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4807-C

Abstract

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.