Deformed Macdonald-Ruijsenaars Operators and Super Macdonald Polynomials
β Scribed by A. N. Sergeev; A. P. Veselov
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 288 KB
- Volume
- 288
- Category
- Article
- ISSN
- 0010-3616
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π SIMILAR VOLUMES
We construct explicitly (nonpolynomial) eigenfunctions of the difference operators by Macdonald in the case t=q k , k Β₯ 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