A Hopf laboratory for symmetric functions

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.

29 pages, LaTeX, uses amsmath

References in corpus (6)

• On the Hopf algebraic origin of Wick normal-ordering
• Renormalization as a functor on bialgebras
• A Treatise on Quantum Clifford Algebras
• On an easy transition from operator dynamics to generating functionals by Clifford algebras
• Positronium as an example of algebraic composite calculations
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• The Dirichlet Hopf algebra of arithmetics
• Hopf Algebras, Distributive (Laplace) Pairings and Hash Products: A unified approach to tensor product decompositions of group characters
• Some graphical aspects of Frobenius structures
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• Systematics and symmetry in molecular phylogenetic modelling: perspectives from physics
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