Invariant differential operators on the Heisenberg group and Meixner-Pollaczek polynomials

Jacques Faraut, Masato Wakayama

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Consider the Heisenberg Lie algebra with basis X, Y, Z, such that [X, Y] D Z. Then the symmetrization σ(XkYk) can be written as a polynomial in σ(XY) and Z, and this polynomial is identified as a Meixner-Pollaczek polynomial. This is an observation by Bender, Mead and Pinsky, a proof of which has been given by Koornwinder. We extend this result in the framework of Gelfand pairs associated with the Heisenberg group. This extension involves multivariable Meixner-Pollaczek polynomials.

Original languageEnglish
Pages (from-to)41-66
Number of pages26
JournalAdvances in Pure and Applied Mathematics
Volume4
Issue number1
DOIs
Publication statusPublished - Apr 1 2013

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Meixner Polynomials
Invariant Differential Operators
Heisenberg Group
Gelfand Pairs
Heisenberg Algebra
Polynomial
Symmetrization
Lie Algebra
Framework
Observation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Invariant differential operators on the Heisenberg group and Meixner-Pollaczek polynomials. / Faraut, Jacques; Wakayama, Masato.

In: Advances in Pure and Applied Mathematics, Vol. 4, No. 1, 01.04.2013, p. 41-66.

Research output: Contribution to journalArticle

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