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 expr
Combinatorial formula for Macdonald polynomials and generic Macdonald polynomials
✍ Scribed by Andrei Okounkov
- Publisher
- SP Birkhäuser Verlag Boston
- Year
- 2003
- Tongue
- English
- Weight
- 168 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1083-4362
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📜 SIMILAR VOLUMES
We construct explicitly (nonpolynomial) eigenfunctions of the difference operators by Macdonald in the case t=q k , k ¥ Z. This leads to a new, more elementary proof of several Macdonald conjectures, proved first by Cherednik. We also establish the algebraic integrability of Macdonald operators at t
In the basic representation of U q ( sl @ 2 ) realized via the algebra of symmetric functions, we compare the canonical basis with the basis of Macdonald polynomials where t=q 2 . We show that the Macdonald polynomials are invariant with respect to the bar involution defined abstractly on the repres