Positivity of Shimura operators

Siddhartha Sahi, Genkai Zhang

Research output: Contribution to journalReview articlepeer-review

1 Scopus citations


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’s questions.

Original languageEnglish (US)
Pages (from-to)587-626
Number of pages40
JournalMathematical Research Letters
Issue number2
StatePublished - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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