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

Jacques Faraut, Masato Wakayama

研究成果: Contribution to journalArticle査読

3 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)41-66
ページ数26
ジャーナルAdvances in Pure and Applied Mathematics
4
1
DOI
出版ステータス出版済み - 4 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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