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This article is cited in 43 scientific papers (total in 43 papers)
Anisotropic Young Diagrams and Jack Symmetric Functions
S. V. Kerov St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
We study the Young lattice with the edge multiplicities $\varkappa_\alpha(\lambda,\Lambda)$ arising in the simplest Pieri formula for Jack symmetric polynomials $P_\lambda(x;\alpha)$ with parameter $\alpha$. A new proof of Stanley's $\alpha$-version of the hook formula is given. We also prove the formula
$$
\sum_\Lambda (c_\alpha(b)+u)(c_\alpha(b)+v)\varkappa_\alpha(\lambda,\Lambda)\varphi(\Lambda)=
(n\alpha+uv)\varphi(\lambda),
$$
where $\varphi(\lambda)=\prod_{b\in\lambda}(a(b)\alpha+l(b)+1)^{-1}$ and $c_\alpha(b)$ is the $\alpha$-contents of the new box $b=\Lambda\setminus\lambda$.
Received: 05.05.1998
Citation:
S. V. Kerov, “Anisotropic Young Diagrams and Jack Symmetric Functions”, Funktsional. Anal. i Prilozhen., 34:1 (2000), 51–64; Funct. Anal. Appl., 34:1 (2000), 41–51
Linking options:
https://www.mathnet.ru/eng/faa282https://doi.org/10.4213/faa282 https://www.mathnet.ru/eng/faa/v34/i1/p51
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