Abstract
We show that the specialization of nonsymmetric Macdonald polynomials at t = 0 are, up to multiplication by a simple factor, characters of Demazure modules for \(\widehat{sl(n)}\). This connection furnishes Lie-theoretic proofs of the nonnegativity and monotonicity of Kostka polynomials.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
L.M. Butler, “Subgroup lattices and symmetric functions,” Memoirs of the A.M.S 112(539), (1994).
I. Cherednik, “Double affine Hecke algebras and Macdonald' conjectures,” Ann. Math. 141 (1995), 191–216.
M. Demazure, “Désingularisation des variétés de Schubert généralisées,” Ann. Scient. Ec. Norm. Sup. 6 (1974), 53–88.
A. Garsia and C. Procesi, “On certain graded S n-modules and the q-Kostka polynomials,” Adv. Math 94(1) (1992), 82–138.
A.N. Kirillov, “Dilogarithm identities,” hep-th/9408113 v2, 25, Aug 1994.
F. Knop, “Integrality of two variable Kostka functions,” J. reine angew. Math. 482 (1997), 177–189.
S. Kumar, “Demazure character formula in arbitrary Kac-Moody setting,” Invent. Math. 89 (1987), 395–423.
A. Kuniba, K.C. Misra, M. Okado, T. Takagi, and J. Uchiyama, “Characters of Demazure modules and solvable lattice models,” q-alg 9707004, 3 July 1997.
A. Lascoux and M.-P. Schützenberger, “Sur une conjecture de H. O. Foulkes,” C.R. Acad. Sci. Paris 286A (1978), no. 7, 323–324.
G. Lusztig, “Green polynomials and singularities of unipotent classes,” Advances in Math. 42 (1981), 169–178.
I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition, Oxford Math. Mon. Clarendon Press, Oxford, 1995.
I.G. Macdonald, “Affine Hecke algebras and orthogonal polynomials,” Seminaire Bourbaki, 1996, Vol. 1994/1995, Astérisque No. 237, Exp. No. 797, 4, 189–207.
O. Mathieu, “Formule de Demazure-Weyl et généralisation du théorè me de Borel-Weil-Bott,” C.R. Acad. Sci. Paris, S´er. I Math. 303(9) (1986), 391–394.
E. Opdam, “Harmonic analysis for certain representations of graded Hecke algebras,” Acta Math. 175 (1995), 75–121.
Y. Sanderson, “Real characters of Demazure modules for rank two affine Lie algebras,” J. Algebra 184 (1996), 985–1000.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sanderson, Y.B. On the Connection Between Macdonald Polynomials and Demazure Characters. Journal of Algebraic Combinatorics 11, 269–275 (2000). https://doi.org/10.1023/A:1008786420650
Issue Date:
DOI: https://doi.org/10.1023/A:1008786420650