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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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Wreath Macdonald polynomials at $q=t$ as characters of rational Cherednik algebras
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by Dario Mathiä and Ulrich Thiel PDF
Trans. Amer. Math. Soc. 375 (2022), 8945-8968 Request permission

Abstract:

Using the theory of Macdonald [Symmetric functions and Hall polynomials, The Clarendon Press, Oxford University Press, New York, 1995], Gordon [Bull. London Math. Soc. 35 (2003), pp. 321–336] showed that the graded characters of the simple modules for the restricted rational Cherednik algebra by Etingof and Ginzburg [Invent. Math. 147 (2002), pp. 243–348] associated to the symmetric group $\mathfrak {S}_n$ are given by plethystically transformed Macdonald polynomials specialized at $q=t$. We generalize this to restricted rational Cherednik algebras of wreath product groups $C_\ell \wr \mathfrak {S}_n$ and prove that the corresponding characters are given by a specialization of the wreath Macdonald polynomials defined by Haiman in [Combinatorics, symmetric functions, and Hilbert schemes, Int. Press, Somerville, MA, 2003, pp. 39–111].
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Additional Information
  • Dario Mathiä
  • Affiliation: Fachbereich Mathematik, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
  • Email: mathiae@mathematik.uni-kl.de
  • Ulrich Thiel
  • Affiliation: Fachbereich Mathematik, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
  • MR Author ID: 1078826
  • Email: thiel@mathematik.uni-kl.de
  • Received by editor(s): January 10, 2022
  • Received by editor(s) in revised form: June 24, 2022
  • Published electronically: August 30, 2022
  • Additional Notes: This work was a contribution to Project-ID 286237555 – TRR 195 – by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation).
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 8945-8968
  • MSC (2020): Primary 16Gxx, 05Exx
  • DOI: https://doi.org/10.1090/tran/8774