The Boundary of Young Graph with Jack Edge Multiplicities

  title={The Boundary of Young Graph with Jack Edge Multiplicities},
  author={Andrei Okounkov},
  • Andrei Okounkov
  • Published 1997
Consider the lattice of all Young diagrams ordered by inclusion, and denote by Y its Hasse graph. Using the Pieri formula for Jack symmetric polynomials, we endow the edges of the graph Y with formal multiplicities depending on a real parameter θ. The multiplicities determine a potential theory on the graph Y. Our main result identifies the corresponding Martin boundary with an infinite-dimensional simplex, the “geometric boundary” of the Young graph Y, and provides a canonical integral… CONTINUE READING
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