A combinatorial formula for Macdonald polynomials
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- by J. Haglund, M. Haiman and N. Loehr PDF
- J. Amer. Math. Soc. 18 (2005), 735-761 Request permission
Abstract:
We prove a combinatorial formula for the Macdonald polynomial $\tilde {H}_{\mu }(x;q,t)$ which had been conjectured by Haglund. Corollaries to our main theorem include the expansion of $\tilde {H}_{\mu }(x;q,t)$ in terms of LLT polynomials, a new proof of the charge formula of Lascoux and Schützenberger for Hall-Littlewood polynomials, a new proof of Knop and Sahi’s combinatorial formula for Jack polynomials as well as a lifting of their formula to integral form Macdonald polynomials, and a new combinatorial rule for the Kostka-Macdonald coefficients $\tilde {K}_{\lambda \mu }(q,t)$ in the case that $\mu$ is a partition with parts $\leq 2$.References
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Additional Information
- J. Haglund
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
- MR Author ID: 600170
- Email: jhaglund@math.upenn.edu
- M. Haiman
- Affiliation: Department of Mathematics, University of California, Berkeley, California 97420-3840
- N. Loehr
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
- Address at time of publication: Department of Mathematics, College of William & Mary, Williamsburg, Virginia 23187-8795
- Email: nloehr@math.upenn.edu, nick@math.wm.edu
- Received by editor(s): October 18, 2004
- Published electronically: April 8, 2005
- Additional Notes: The first author’s work was supported by NSA grant MSPF-02G-193
The second author’s work was supported by NSF grant DMS-0301072
The third author’s work was supported by an NSF Postdoctoral Research Fellowship - © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 18 (2005), 735-761
- MSC (2000): Primary 05E10; Secondary 05A30
- DOI: https://doi.org/10.1090/S0894-0347-05-00485-6
- MathSciNet review: 2138143