Holonomic systems of Gegenbauer type polynomials of matrix arguments related with Siegel modular forms

DOI10.2969/jmsj/06410273zbMath1272.11066OpenAlexW2051567025MaRDI QIDQ763989

Tomoyoshi Ibukiyama, Takako Kuzumaki, Hiroyuki Ochiai

Publication date: 3 April 2012

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2969/jmsj/06410273

zbMATH Keywords

holonomic systemdifferential operatorsSiegel modular forms

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Sheaves of differential operators and their modules, (D)-modules (32C38) Hecke-Petersson operators, differential operators (several variables) (11F60) Hypergeometric functions associated with root systems (33C67)

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Differential symmetry breaking operators. II: Rankin-Cohen operators for symmetric pairs ⋮ Differential operators, exact pullback formulas of Eisenstein series, and Laplace transforms ⋮ A geometrical point of view for branching problems for holomorphic discrete series of conformal Lie groups ⋮ Covariant bi-differential operators on matrix space ⋮ Computation of weighted Bergman inner products on bounded symmetric domains and restriction to subgroups ⋮ The holonomic gradient method for the distribution function of the largest root of a Wishart matrix ⋮ Computation of weighted Bergman inner products on bounded symmetric domains and Parseval-Plancherel-type formulas under subgroups ⋮ Harder's conjecture. I ⋮ Generic differential operators on Siegel modular forms and special polynomials ⋮ Algebraic analysis of the hypergeometric function \(_1F_1\) of a matrix argument ⋮ One-line formula for automorphic differential operators on Siegel modular forms

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