An explicit construction of type A Demazure atoms
S. Mason
Department of Mathematics, Davidson College, Davidson, USA
DOI: 10.1007/s10801-008-0133-4
Abstract
Demazure characters of type A, which are equivalent to key polynomials, have been decomposed by Lascoux and Schützenberger into standard bases. We prove that the resulting polynomials, which we call Demazure atoms, can be obtained from a certain specialization of nonsymmetric Macdonald polynomials. This combinatorial interpretation for Demazure atoms accelerates the computation of the right key associated to a semi-standard Young tableau. Utilizing a related construction, we provide a new combinatorial description of the key polynomials.
Pages: 295–313
Keywords: keywords symmetric functions; Young tableaux; Demazure characters
Full Text: PDF
References
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2. Haglund, J., Haiman, M., Loehr, N.: A combinatorial formula for nonsymmetric Macdonald polynomials. Preprint arXiv.org/abs/math.CO/0601693 (2005)
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8. Knuth, D.E.: Permutations matrices, and generalized Young tableaux. Pac. J. Math. 34, 709-727 (1970)
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10. Mason, S.: A decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth algorithm. arXiv:math.CO/0604430 (2006)
11. Reiner, V., Shimozono, M.: Key polynomials and a flagged Littlewood-Richardson rule. J. Comb.
2. Haglund, J., Haiman, M., Loehr, N.: A combinatorial formula for nonsymmetric Macdonald polynomials. Preprint arXiv.org/abs/math.CO/0601693 (2005)
3. Haglund, J., Mason, S., Remmel, J.: Properties of an analogue of the Robinson-Schensted-Knuth Algorithm. Preprint (2007)
4. Ion, B.: Nonsymmetric Macdonald polynomials and Demazure characters. Duke Math. J. 116, 299- 318 (2003)
5. Joseph, A.: On the Demazure character formula. Ann. Sci. Ec. Norm. Super. (4) 18(3), 389-419 (1985)
6. Kashiwara, M.: Crystalizing the q-analogue of Universal Enveloping Algebras. Commun. Math. Phys. 133, 249-260 (1990)
7. Kashiwara, M.: The crystal base and Littelmann's refined Demazure character formula. Duke Math. J. 71(3), 839-858 (1993)
8. Knuth, D.E.: Permutations matrices, and generalized Young tableaux. Pac. J. Math. 34, 709-727 (1970)
9. Lascoux, A., Schützenberger, M.-P.: Keys and standard bases. In: Stanton, D. (ed.) Invariant Theory and Tableaux. IMA Volumes in Math. and Its Applications, vol. 19, pp. 125-144. Springer, Berlin (1990)
10. Mason, S.: A decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth algorithm. arXiv:math.CO/0604430 (2006)
11. Reiner, V., Shimozono, M.: Key polynomials and a flagged Littlewood-Richardson rule. J. Comb.