In prior work an orbit method, due to Pukanszky and Lipsman, was used to produce an injective mapping $\Psi\colon \Delta(K,N)\rightarrow\mathfrak{n}^*/K$ from the space of bounded $K$-spherical functions for a nilpotent Gelfand pair $(K,N)$ into the space of $K$-orbits in the dual for the Lie algebra $\mathfrak{n}$ of $N$. We have conjectured that $\Psi$ is a topological embedding. In this paper we complete the proof of this conjecture under the hypothesis that $(K,N)$ is an {\it irreducible} nilpotent Gelfand pair. Following Part I of this work it remains to verify the conjecture in six exceptional cases from Vinberg's classification of irreducible nilpotent Gelfand pairs.
1
Dept. of Mathematics, East Carolina University, Greenville, NC 27858, U.S.A.
Chal Benson; Gail Ratcliff. Spaces of Bounded Spherical Functions for Irreducible Nilpotent Gelfand Pairs: Part II. Journal of Lie Theory, Tome 31 (2021) no. 2, pp. 367-392. http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a4/
@article{JOLT_2021_31_2_a4,
author = {Chal Benson and Gail Ratcliff},
title = {Spaces of {Bounded} {Spherical} {Functions} for {Irreducible} {Nilpotent} {Gelfand} {Pairs:} {Part} {II}},
journal = {Journal of Lie Theory},
pages = {367--392},
year = {2021},
volume = {31},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a4/}
}
TY - JOUR
AU - Chal Benson
AU - Gail Ratcliff
TI - Spaces of Bounded Spherical Functions for Irreducible Nilpotent Gelfand Pairs: Part II
JO - Journal of Lie Theory
PY - 2021
SP - 367
EP - 392
VL - 31
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a4/
ID - JOLT_2021_31_2_a4
ER -
%0 Journal Article
%A Chal Benson
%A Gail Ratcliff
%T Spaces of Bounded Spherical Functions for Irreducible Nilpotent Gelfand Pairs: Part II
%J Journal of Lie Theory
%D 2021
%P 367-392
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a4/
%F JOLT_2021_31_2_a4
