Vector valued spherical functions and Macdonald-Koornwinder polynomials

Alexei Oblomkov; Jasper V. Stokman

doi:10.48550/arxiv.math/0311512

November 27, 2003Open Access

Vector valued spherical functions and Macdonald-Koornwinder polynomials

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Key Points

Establish an algebraic and geometric interpretation of the five-parameter family of Macdonald-Koornwinder polynomials through quantum spaces.
Analyzed representation theory and harmonic analysis on quantum Grassmannian spaces.
Formulated multivariable polynomial systems in the framework of vector-valued spherical functions.
Demonstrated that the five-parameter family of Macdonald-Koornwinder polynomials corresponds directly to vector-valued spherical functions on quantum Grassmannians.
Connected multivariable orthogonal polynomial theory with non-commutative quantum geometry.

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Implication

Theoretical analysis reveals Macdonald-Koornwinder polynomials as spherical functions on quantum Grassmannians, highlighting geometric interpretations for multivariable orthogonal polynomials.

Abstract

We interpret the five parameter family of Macdonald-Koornwinder polynomials as vector valued spherical functions on quantum Grassmannians.

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Oblomkov et al. (2003) studied this question.

synapsesocial.com/papers/6a75d04920e137e1c1162682 https://doi.org/10.48550/arxiv.math/0311512

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Vector valued spherical functions and Macdonald-Koornwinder polynomials

Key Points

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Abstract

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Vector valued spherical functions and Macdonald-Koornwinder polynomials

Key Points

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