On vertex operator realizations of Jack functions

DOI10.1007/s10801-010-0228-6zbMath1221.17031arXiv1002.1350OpenAlexW1993634146WikidataQ57438280 ScholiaQ57438280MaRDI QIDQ604833

Naihuan Jing, Wu Xing Cai

Publication date: 12 November 2010

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.1350

zbMATH Keywords

symmetric functionsvertex operatorsJack polynomials

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Vertex operators; vertex operator algebras and related structures (17B69) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)

Related Items (7)

\(S\)-functions, spectral functions of hyperbolic geometry, and vertex operators with applications to structure for Weyl and orthogonal group invariants ⋮ Deformation of Cayley's hyperdeterminants ⋮ Applications of a Laplace-Beltrami operator for Jack polynomials ⋮ Jack vertex operators and realization of Jack functions ⋮ Macdonald symmetric functions of rectangular shapes ⋮ A generalization of Newton's identity and Macdonald functions ⋮ Principal subspaces for the affine Lie algebras in types \(D, E\) and \(F\)

Cites Work

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• A formula for two-row Macdonald functions
• A Macdonald vertex operator and standard tableaux statistics for the two-column \((q,t)\)-Kosta coefficients
• \(q\)-hypergeometric series and Macdonald functions
• Some combinatorial properties of Jack symmetric functions
• Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials

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