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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Nonsymmetric Macdonald polynomials and a refinement of Kostka–Foulkes polynomials
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by Sami Assaf PDF
Trans. Amer. Math. Soc. 370 (2018), 8777-8796


We study the specialization of the type A nonsymmetric Macdonald polynomials at $t=0$ based on the combinatorial formula of Haglund, Haiman, and Loehr. We prove that this specialization expands nonnegatively into the fundamental slide polynomials, introduced by the author and Searles. Using this and weak dual equivalence, we prove combinatorially that this specialization is a positive graded sum of Demazure characters. We use stability results for fundamental slide polynomials to show that this specialization stabilizes and to show that the Demazure character coefficients give a refinement of the Kostka–Foulkes polynomials.
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Additional Information
  • Sami Assaf
  • Affiliation: Department of Mathematics, University of Southern California, 3620 S. Vermont Avenue, Los Angeles, California 90089-2532
  • MR Author ID: 775302
  • Email:
  • Received by editor(s): March 7, 2017
  • Received by editor(s) in revised form: March 9, 2017, and August 16, 2017
  • Published electronically: July 31, 2018
  • © Copyright 2018 by Sami Assaf
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 8777-8796
  • MSC (2010): Primary 33D52; Secondary 05E05
  • DOI:
  • MathSciNet review: 3864395