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

 IBUKIYAMA Tomoyoshi IBUKIYAMA Tomoyoshi
 Department of Mathematics, Graduate School of Science, Osaka University

 KUZUMAKI Takako KUZUMAKI Takako
 Department of Mathematical and Design Engineering, Faculty of Engineering, Gifu University

 OCHIAI Hiroyuki OCHIAI Hiroyuki
 Faculty of Mathematics, Kyushu University
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Author(s)

 IBUKIYAMA Tomoyoshi IBUKIYAMA Tomoyoshi
 Department of Mathematics, Graduate School of Science, Osaka University

 KUZUMAKI Takako KUZUMAKI Takako
 Department of Mathematical and Design Engineering, Faculty of Engineering, Gifu University

 OCHIAI Hiroyuki OCHIAI Hiroyuki
 Faculty of Mathematics, Kyushu University
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 2<i>n</i> to the product of degree <i>n</i>. These generalize the Gegenbauer polynomials which appear for <i>n</i> = 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<sup><i>n</i></sup>.
Journal

 Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 64(1), 273316, 20120101
The Mathematical Society of Japan
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