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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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New identities for theta operators
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by Michele D’Adderio and Marino Romero
Trans. Amer. Math. Soc. 376 (2023), 5775-5807
DOI: https://doi.org/10.1090/tran/8911
Published electronically: May 9, 2023

Abstract:

In this article, we prove a new general identity involving the Theta operators introduced by the first author, Iraci, and Vanden Wyngaerd [Adv. Math. 376 (2021), p.59]. From this result, we can easily deduce several new identities that have combinatorial consequences in the study of Macdonald polynomials and diagonal coinvariants. In particular, we provide a unifying framework from which we recover many identities scattered in the literature, often resulting in drastically shorter proofs.
References
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Bibliographic Information
  • Michele D’Adderio
  • Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
  • MR Author ID: 861645
  • Email: michele.dadderio@unipi.it
  • Marino Romero
  • Affiliation: Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab., 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395
  • MR Author ID: 1173529
  • Email: mar007@sas.upenn.edu
  • Received by editor(s): January 7, 2021
  • Received by editor(s) in revised form: February 2, 2023
  • Published electronically: May 9, 2023
  • Additional Notes: The first author was partially supported by the Fonds Thelam project J1150080.
    The second author was partially supported by the University of California President’s Postdoctoral Fellowship.
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 5775-5807
  • MSC (2020): Primary 05E05; Secondary 20C30
  • DOI: https://doi.org/10.1090/tran/8911
  • MathSciNet review: 4630759