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Rodrigues Formulas for the Macdonald Polynomials

โœ Scribed by Luc Lapointe; Luc Vinet

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
368 KB
Volume
130
Category
Article
ISSN
0001-8708

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โœฆ Synopsis

We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions * through the repeated application of creation operators B k , k=1, ..., l (*) on the constant 1. Three expressions for the creation operators are derived one from the other. When the last of these expressions is used, the associated Rodrigues formula readily implies the integrality of the (q, t)-Kostka coefficients. The proofs given in this paper rely on the connection between affine Hecke algebras and Macdonald polynomials. 1997 Academic Press k was given as a conjecture. This third expression was also found by Kirillov and Noumi who provided two article no. AI971662 261

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