@article{be228618c6ee45a29d40ad847a04119c,
title = "Positivity of Shimura operators",
abstract = "In this paper we answer some questions of G. Shimura on the positivity of certain invariant differential operators that play a key role in the study of nearly holomorphic automorphic forms in higher rank. Our main result expresses the eigenvalues of Shimura operators in terms of certain polynomials introduced by A. Okounkov, which leads to an explicit answer to Shimura{\textquoteright}s questions.",
author = "Siddhartha Sahi and Genkai Zhang",
note = "Funding Information: Research by Genkai Zhang was partially supported by the Swedish Science Council (VR). Siddhartha Sahi was partially supported by an AIP research grant from Rutgers University and by the Simons Foundation. Part of this work was done when Genkai Zhang was visiting the Korea Institute for Advanced Study (KIAS) as a KIAS scholar in April 2016, he would like to thank the institute for its support and hospitality. Both authors thank Tom Koornwinder for helpful correspondence. We also thank Alejandro Ginory for computational assistance, which was extremely helpful at an early stage of this project. Publisher Copyright: {\textcopyright} 2019 International Press of Boston, Inc.. All rights reserved.",
year = "2019",
doi = "10.4310/MRL.2019.v26.n2.a9",
language = "English (US)",
volume = "26",
pages = "587--626",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "International Press, Inc.",
number = "2",
}