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

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Author(s)

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), 273-316, 2012-01-01

    The Mathematical Society of Japan

References:  20

Codes

  • NII Article ID (NAID)
    10030740141
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    023404142
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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