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

Tomoyoshi Ibukiyama, Takako Kuzumaki, Hiroyuki Ochiai

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5 Citations (Scopus)

Abstract

Differential operators on Siegel modular forms which behave well under the restriction of the domain are essentially intertwining operators of the tensor product of holomorphic discrete series to its irreducible components. These are characterized by polynomials in the tensor of pluriharmonic polynomials with some invariance properties. We give a concrete study of such polynomials in the case of the restriction from Siegel upper half space of degree 2n to the product of degree n. These generalize the Gegenbauer polynomials which appear for n = 1. We also describe their radial parts parametrization and differential equations which they satisfy, and show that these differential equations give holonomic systems of rank 2 n.

Original languageEnglish
Pages (from-to)273-316
Number of pages44
JournalJournal of the Mathematical Society of Japan
Volume64
Issue number1
DOIs
Publication statusPublished - Oct 5 2012

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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