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Rodrigues formulas for the Macdonald polynomials. (English) Zbl 0986.33012
The authors here present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions \(\lambda\) through the repeated application of creation operators \(B_k\), \(k= 1,\dots,\ell(\lambda)\) on the constant 1. Three expressions for the creation operators are associated. Rodrigues formula readily implies the integrality of the \((q,t)\)-Kostka coefficients. The proofs rely on the connection between affine Hecke algebras and Macdonald polynomials.

MSC:
33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
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