Abstract
We study the Young lattice with the edge multiplicitiesϰ α (λ, ⋏) arising in the simplest Pieri formula for Jack symmetric polynomialsP λ (x; α) with parameter α. A new proof of Stanley’s α-version of the hook formula is given. We also prove the formula
whereϕ(λ) = ∏ b∈λ (a(b)α +l(b) + 1)−1 andc α(b) is the α-contents of the new boxb=⋏/λ.
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Additional information
Partially supported by the Federal Grant Program “Integration,” No. 326.53, and by MSRI at Berkeley.
St. Petersburg Division of the V. A. Steklov Mathematical Institute. Translated from Funksional’nyi Analiz i Ego Prilozheniya, Vol. 34, No. 1, pp. 51–64, January–March, 200.
Translated by S. V. Kerov
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Kerov, S.V. Anisotropic young diagrams and jack symmetric functions. Funct Anal Its Appl 34, 41–51 (2000). https://doi.org/10.1007/BF02467066
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DOI: https://doi.org/10.1007/BF02467066