Mason, S. An explicit construction of type A Demazure atoms. (English) Zbl 1210.05175 J. Algebr. Comb. 29, No. 3, 295-313 (2009). Summary: 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. Cited in 1 ReviewCited in 25 Documents MSC: 05E05 Symmetric functions and generalizations 05E10 Combinatorial aspects of representation theory Keywords:symmetric functions; Young tableaux; Demazure characters; decomposition; Demazure atoms PDF BibTeX XML Cite \textit{S. Mason}, J. Algebr. Comb. 29, No. 3, 295--313 (2009; Zbl 1210.05175) Full Text: DOI References: [1] Demazure, M.: Désingularisation des variétés de Schubert. Ann. Sci. Ec. Norm. Super. 6, 163-172 (1974) [2] Haglund, J., Haiman, M., Loehr, N.: A combinatorial formula for nonsymmetric Macdonald polynomials. Preprint arXiv.org/abs/math.CO/0601693 (2005) · Zbl 1061.05101 [3] Haglund, J., Mason, S., Remmel, J.: Properties of an analogue of the Robinson-Schensted-Knuth Algorithm. Preprint (2007) · Zbl 1271.05100 [4] Ion, B., Nonsymmetric Macdonald polynomials and Demazure characters, Duke Math. J., 116, 299-318, (2003) · Zbl 1039.33008 [5] Joseph, A., On the Demazure character formula, Ann. Sci. Ec. Norm. Super. (4), 18, 389-419, (1985) · Zbl 0589.22014 [6] Kashiwara, M., Crystalizing the \(q\)-analogue of Universal Enveloping Algebras, Commun. Math. Phys., 133, 249-260, (1990) · Zbl 0724.17009 [7] Kashiwara, M., The crystal base and Littelmann’s refined Demazure character formula, Duke Math. J., 71, 839-858, (1993) · Zbl 0794.17008 [8] Knuth, D. E., Permutations matrices, and generalized Young tableaux, Pac. J. Math., 34, 709-727, (1970) · Zbl 0199.31901 [9] Lascoux, A.; Schützenberger, M.-P.; Stanton, D. (ed.), Keys and standard bases, No. 19, 125-144, (1990), Berlin · Zbl 0815.20013 [10] Mason, S.: A decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth algorithm. arXiv:math.CO/0604430 (2006) · Zbl 1193.05160 [11] Reiner, V.; Shimozono, M., Key polynomials and a flagged Littlewood-Richardson rule, J. Comb. Theory Ser. A, 70, 107-143, (1995) · Zbl 0819.05058 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.