Orthogonality of Macdonald polynomials with unitary parameters

Abstract

For any admissible pair of irreducible reduced crystallographic root systems, we present discrete orthogonality relations for a finite-dimensional system of Macdonald polynomials with parameters on the unit circle subject to a truncation relation.

26 pages, updated references, correction of typos. To appear in Math. Z

References in corpus (1)

• Discrete harmonic analysis on a Weyl alcove

Cited by in corpus (6)

• Cubature formulas of multivariate polynomials arising from symmetric orbit functions
• Generalized discrete orbit function transforms of affine Weyl groups
• Discrete cosine and sine transforms generalized to honeycomb lattice
• Trigonometric and elliptic Ruijsenaars-Schneider systems on the complex projective space
• Quantization and explicit diagonalization of new compactified trigonometric Ruijsenaars-Schneider systems
• Integrable many-body systems of Calogero-Ruijsenaars type