Symmetric polynomials, generalized Jacobi-Trudi identities and τ-functions

@article{Harnad2013SymmetricPG,
  title={Symmetric polynomials, generalized Jacobi-Trudi identities and τ-functions},
  author={J. Harnad and E. Lee},
  journal={Journal of Mathematical Physics},
  year={2013},
  volume={59},
  pages={091411}
}
  • J. Harnad, E. Lee
  • Published 2013
  • Mathematics, Physics
  • Journal of Mathematical Physics
An element [Φ]∈GrnH+,F of the Grassmannian of n-dimensional subspaces of the Hardy space H+=H2, extended over the field F = C(x1, …, xn), may be associated to any polynomial basis ϕ = {ϕ0, ϕ1, ⋯ } for C(x). The Plucker coordinates Sλ,nϕ(x1,…,xn) of [Φ], labeled by partitions λ, provide an analog of Jacobi’s bi-alternant formula, defining a generalization of Schur polynomials. Applying the recursion relations satisfied by the polynomial system ϕ to the analog {hi(0)} of the complete symmetric… Expand
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