Asymptotic spherical analysis on the Heisenberg group

• Autorzy: Jacques Faraut
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 22E27: Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
• 33C50: Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
• 43A90: Spherical functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 1
• Strony: 233-258

Daty

wydano

2010

Twórcy

autor

Jacques Faraut

• Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris, France

Identyfikatory

DOI

10.4064/cm118-1-13