Pieri formulas for Macdonald's spherical functions and polynomials

DOI10.1007/s00209-010-0727-0zbMath1291.05212arXiv1009.4482OpenAlexW3103605539MaRDI QIDQ641865

E. Emsiz, Jan Felipe van Diejen

Publication date: 25 October 2011

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.4482

zbMATH Keywords

symmetric functionsroot systemsMacdonald polynomialsreflection groupsHall-Littlewood polynomialsPieri formulas

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Root systems (17B22)

Related Items

2d TQFT structure of the superconformal indices with outer-automorphism twists ⋮ A Littlewood-Richardson rule for Macdonald polynomials ⋮ A Pieri formula for the characters of complex simple Lie algebras ⋮ Unitary representations of affine Hecke algebras related to Macdonald spherical functions ⋮ An elliptic hypergeometric function approach to branching rules ⋮ Orthogonal polynomials of compact simple Lie groups

Cites Work

• Haglund-Haiman-Loehr type formulas for Hall-Littlewood polynomials of type B and C
• Hall-Littlewood polynomials, alcove walks, and fillings of Young diagrams
• Alcove walks, Hecke algebras, spherical functions, crystals and column strict tableaux.
• An (inverse) Pieri formula for Macdonald polynomials of type \(C\)
• Kernel functions for difference operators of Ruijsenaars type and their applications
• Difference equations and Pieri formulas for \(G_2\) type Macdonald polynomials and integrability
• The partial order of dominant weights
• Orthogonal polynomials associated with root systems
• Buildings and Hecke algebras.
• Inversion of the Pieri formula for Macdonald polynomials
• Affine insertion and Pieri rules for the affine Grassmannian
• Pieri-Type Formulas for Nonsymmetric Macdonald Polynomials
• Galleries, Hall-Littlewood polynomials, and structure constants of the spherical Hecke algebra
• Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber
• Commuting difference operators with polynomial eigenfunctions
• A Note on the Multiplication of Hall Functions
• Giambelli, Pieri, and tableau formulas via raising operators
• Self-dual Koornwinder-Macdonald polynomials
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