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

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概要

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• 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 2n.

• 2012-01-01

著者

• KUZUMAKI Takako

  Department of Electrical Engineering Faculty of Engineering Gifu University

• Ibukiyama Tomoyoshi

  Department Of Mathematics College Of General Education Osaka University

• Ochiai Hiroyuki

  Faculty Of Mathematics Kyushu University

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