TY - JOUR
T1 - Invariant differential operators on the Heisenberg group and Meixner-Pollaczek polynomials
AU - Faraut, Jacques
AU - Wakayama, Masato
PY - 2013/4
Y1 - 2013/4
N2 - 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.
AB - 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.
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U2 - 10.1515/apam-2013-0204
DO - 10.1515/apam-2013-0204
M3 - Article
AN - SCOPUS:84878316166
SN - 1867-1152
VL - 4
SP - 41
EP - 66
JO - Advances in Pure and Applied Mathematics
JF - Advances in Pure and Applied Mathematics
IS - 1
ER -