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      A Hopf laboratory for symmetric functions

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          Abstract

          An analysis of symmetric function theory is given from the perspective of the underlying Hopf and bi-algebraic structures. These are presented explicitly in terms of standard symmetric function operations. Particular attention is focussed on Laplace pairing, Sweedler cohomology for 1- and 2-cochains, and twisted products (Rota cliffordizations) induced by branching operators in the symmetric function context. The latter are shown to include the algebras of symmetric functions of orthogonal and symplectic type. A commentary on related issues in the combinatorial approach to quantum field theory is given.

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          Author and article information

          Journal
          29 August 2003
          Article
          10.1088/0305-4470/37/5/012
          math-ph/0308043
          c784f650-bede-4369-8c2d-539ba89580c1
          History
          Custom metadata
          05E05;16W30;20G10;11E57
          UTAS-PHYS-2003-02
          J.Phys.A37:1633-1664,2004
          29 pages, LaTeX, uses amsmath
          math-ph hep-th math.MP math.QA

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