, Volume 34, Issue 1, pp 41-51

Anisotropic young diagrams and jack symmetric functions

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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) = ∏ bλ (a(b)α +l(b) + 1)−1 andc α(b) is the α-contents of the new boxb=⋏/λ.

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