Abstract
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.
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© 1996 Kluwer Academic Publishers
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Feinsilver, P., Schott, R. (1996). Canonical systems in several variables. In: Algebraic Structures and Operator Calculus. Mathematics and Its Applications, vol 347. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0157-5_5
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DOI: https://doi.org/10.1007/978-94-009-0157-5_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6557-3
Online ISBN: 978-94-009-0157-5
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