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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Demazure crystals for Kohnert polynomials
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by Sami H. Assaf PDF
Trans. Amer. Math. Soc. 375 (2022), 2147-2186

Abstract:

Kohnert polynomials are polynomials indexed by unit cell diagrams in the first quadrant defined earlier by the author and Searles that give a common generalization of Schubert polynomials and Demazure characters for the general linear group. Demazure crystals are certain truncations of normal crystals whose characters are Demazure characters. For each diagram satisfying a southwest condition, we construct a Demazure crystal whose character is the Kohnert polynomial for the given diagram, resolving an earlier conjecture of the author and Searles that these polynomials expand nonnegatively into Demazure characters. We give explicit formulas for the expansions with applications including a characterization of those diagrams for which the corresponding Kohnert polynomial is a single Demazure character.
References
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Additional Information
  • Sami H. Assaf
  • Affiliation: Department of Mathematics, University of Southern California, 3620 S. Vermont Ave., Los Angeles, California 90089-2532
  • MR Author ID: 775302
  • Email: shassaf@usc.edu
  • Received by editor(s): February 21, 2020
  • Received by editor(s) in revised form: April 8, 2020, and September 13, 2021
  • Published electronically: December 23, 2021
  • Additional Notes: Work supported in part by NSF DMS-1763336
  • © Copyright 2021 by the authors
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 2147-2186
  • MSC (2020): Primary 05E05; Secondary 05E10, 14N15
  • DOI: https://doi.org/10.1090/tran/8560
  • MathSciNet review: 4378090