Positivity of Shimura operators

2016/06/16 by Siddhartha Sahi, Sahi, Siddhartha, Genkai Zhang +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1606.05276

openalex publication_date 2016/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [16] G. Shimura introduced a family of invariant differential operators that play a key role in the study of nearly holomorphic automorphic forms, and he asked for a determination of their \textquotedblleft domain of positivity\textquotedblright. In this paper we relate the eigenvalues of Shimura operators to certain polynomials introduced by A. Okounkov, which leads to an explicit answer to Shimura's questions.

Cited by

• Quadratic Capelli operators and Okounkov polynomials

Related

• Eigenvalues of supersymmetric Shimura operators and interpolation polynomials
• What is Schur positivity and how common is it?
• Positive polynomials in scalar and matrix variables, the spectral theorem and optimization
• Schur polynomials and matrix positivity preservers
• A stabilization theorem for Hermitian forms and applications to holomorphic mappings