Asymptotic spherical analysis on the Heisenberg group

Jacques Faraut. "Asymptotic spherical analysis on the Heisenberg group." Colloquium Mathematicae 118.1 (2010): 233-258. <http://eudml.org/doc/283936>.

@article{JacquesFaraut2010,
abstract = {The asymptotics of spherical functions for large dimensions are related to spherical functions for Olshanski spherical pairs. In this paper we consider inductive limits of Gelfand pairs associated to the Heisenberg group. The group K = U(n) × U(p) acts multiplicity free on 𝓟(V), the space of polynomials on V = M(n,p;ℂ), the space of n × p complex matrices. The group K acts also on the Heisenberg group H = V × ℝ. By a result of Carcano, the pair (G,K) with G = K ⋉ H is a Gelfand pair. The main results of the paper are the asymptotics of the spherical functions related to the pair (G,K) for large n and p. This analysis involves the asymptotics of shifted Schur functions.},
author = {Jacques Faraut},
journal = {Colloquium Mathematicae},
keywords = {Heisenberg group; Spherical function; Fock space; Gelfand pair},
language = {eng},
number = {1},
pages = {233-258},
title = {Asymptotic spherical analysis on the Heisenberg group},
url = {http://eudml.org/doc/283936},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Jacques Faraut
TI - Asymptotic spherical analysis on the Heisenberg group
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 1
SP - 233
EP - 258
AB - The asymptotics of spherical functions for large dimensions are related to spherical functions for Olshanski spherical pairs. In this paper we consider inductive limits of Gelfand pairs associated to the Heisenberg group. The group K = U(n) × U(p) acts multiplicity free on 𝓟(V), the space of polynomials on V = M(n,p;ℂ), the space of n × p complex matrices. The group K acts also on the Heisenberg group H = V × ℝ. By a result of Carcano, the pair (G,K) with G = K ⋉ H is a Gelfand pair. The main results of the paper are the asymptotics of the spherical functions related to the pair (G,K) for large n and p. This analysis involves the asymptotics of shifted Schur functions.
LA - eng
KW - Heisenberg group; Spherical function; Fock space; Gelfand pair
UR - http://eudml.org/doc/283936
ER -