Large n expansion of q -deformed two-dimensional yang-mills theory and hecke algebras

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 dua...

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Bibliographic Details
Published in:Communications in mathematical physics 2007-07, Vol.273 (2), p.317-355
Main Authors: DE HARO, Sebastian, RAMGOOLAM, Sanjaye, TORRIELLI, Alessandro
Format: Article
Language:English
Subjects:
Algebra
Algebraic combinatorics
Combinatorics
Combinatorics. Ordered structures
Deformation
Delta function
Exact sciences and technology
Functional analysis
Group theory
Group theory and generalizations
Mathematical analysis
Mathematical methods in physics
Mathematics
Other topics in mathematical methods in physics
Physics
Riemann surfaces
Sciences and techniques of general use
Yang-Mills theory
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-007-0232-4