Recurrence formulas for Macdonald polynomials of type A
Michel Lassalle
and Michael J. Schlosser
DOI: 10.1007/s10801-009-0207-y
Abstract
We consider products of two Macdonald polynomials of type A, indexed by dominant weights which are respectively a multiple of the first fundamental weight and a weight having zero component on the kth fundamental weight. We give the explicit decomposition of any Macdonald polynomial of type A in terms of this basis.
Pages: 113–131
Keywords: Macdonald polynomials; Pieri formula; multidimensional matrix inverse
Full Text: PDF
References
1. Jing, N.H., Józefiak, T.: A formula for two-row Macdonald functions. Duke Math. J. 67, 377-385 (1992)
2. Lassalle, M.: Explicitation des polynômes de Jack et de Macdonald en longueur trois. C. R. Acad. Sci. Paris Sér. I Math. 333, 505-508 (2001)
3. Lassalle, M., Schlosser, M.J.: Inversion of the Pieri formula for Macdonald polynomials. Adv. Math. 202, 289-325 (2006)
4. Macdonald, I.G.: A new class of symmetric functions. Sém. Lothar. Comb. 20, Article B20a (1988)
5. Macdonald, I.G.: Symmetric Functions and Hall Polynomials, 2nd edn. Clarendon, Oxford (1995)
6. Macdonald, I.G.: Symmetric Functions and Orthogonal Polynomials. University Lecture Series, vol.
12. Am. Math. Soc., Providence (1998)
7. Macdonald, I.G.: Orthogonal polynomials associated with root systems. Sém. Lothar. Comb. 45, Article B45a (2000)
8. Macdonald, I.G.: Affine Hecke Algebras and Orthogonal Polynomials. Oxford University Press, Ox- ford (2003)
9. Perelomov, A.M., Ragoucy, E., Zaugg, P.: Quantum integrable systems and Clebsch-Gordan series: II.
2. Lassalle, M.: Explicitation des polynômes de Jack et de Macdonald en longueur trois. C. R. Acad. Sci. Paris Sér. I Math. 333, 505-508 (2001)
3. Lassalle, M., Schlosser, M.J.: Inversion of the Pieri formula for Macdonald polynomials. Adv. Math. 202, 289-325 (2006)
4. Macdonald, I.G.: A new class of symmetric functions. Sém. Lothar. Comb. 20, Article B20a (1988)
5. Macdonald, I.G.: Symmetric Functions and Hall Polynomials, 2nd edn. Clarendon, Oxford (1995)
6. Macdonald, I.G.: Symmetric Functions and Orthogonal Polynomials. University Lecture Series, vol.
12. Am. Math. Soc., Providence (1998)
7. Macdonald, I.G.: Orthogonal polynomials associated with root systems. Sém. Lothar. Comb. 45, Article B45a (2000)
8. Macdonald, I.G.: Affine Hecke Algebras and Orthogonal Polynomials. Oxford University Press, Ox- ford (2003)
9. Perelomov, A.M., Ragoucy, E., Zaugg, P.: Quantum integrable systems and Clebsch-Gordan series: II.
© 1992–2009 Journal of Algebraic Combinatorics
©
2012 FIZ Karlsruhe /
Zentralblatt MATH for the EMIS Electronic Edition