Canonical systems in several variables

  • Philip Feinsilver
  • René Schott
Part of the Mathematics and Its Applications book series (MAIA, volume 347)


In this chapter we focus on Lie algebras of symmetric type, described in the first section. From these algebras, the quotient representations yield homogeneous spaces, in particular symmetric spaces. The generating functions for the basis of the associated representations are called coherent states. There are connections with the multinomial distribution in probability theory and associated orthogonal polynomials generalizing the Meixner classes to several variables. We conclude with a Fourier technique for constructing new classes of orthogonal systems from certain given systems.


Coherent State Orthogonal Polynomial Homogeneous Space Multinomial Distribution Adjoint Action 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Philip Feinsilver
    • 1
  • René Schott
    • 2
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA
  2. 2.CRINUniversité de Nancy 1Vandoeuvre-les-NancyFrance

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