Explicit Plethystic Formulas for Macdonald q,t-Kostka Coefficients

  title={Explicit Plethystic Formulas for Macdonald q,t-Kostka Coefficients},
  author={M L Garsia and Mark D. Haiman and Glenn Tesler},
i=1 ti−1 (1+· · ·+qμi−1). In [8] Garsia-Tesler proved that if γ is a partition of k and λ = (n−k, γ) is a partition of n, then there is a unique symmetric polynomial kγ(x; q, t) of degree ≤ k with the property that K̃λμ(q, t) = kγ [Bμ(q, t); q, t] holds true for all partitions μ. It was shown there that these polynomials have Schur function expansions of the form kγ(x; q, t) = ∑ |ρ|≤|γ| Sλ(x) kρ,γ(q, t) where the kρ,γ(q, t) are polynomials in q, t, 1/q, 1/t with integer coefficients. This… CONTINUE READING

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