New identities for theta operators

D’Adderio, Michele; Romero, Marino

doi:10.1090/tran/8911

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

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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.

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