Geodesic
Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces
Documenta mathematica, Tome 19 (2014), pp. 1317-1366.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We compute the Harish-Chandra $c$-function for a generic class of rank-one purely non-compact Riemannian symmetric superspaces $X=G/K$ in terms of Euler $\\Gamma$ functions, proving that it is meromorphic. Compared to the even case, the poles of the $c$-function are shifted into the right half-space. We derive the full asymptotic Harish-Chandra series expansion of the spherical superfunctions on $X$. In the case where the multiplicity of the simple root is an even negative number, they have a closed expression as Jacobi polynomials for an unusual choice of parameters.
Classification : 22E45, 17B15, 58A50
Keywords: harish-chandra c-function, Lie supergroup, Riemannian symmetric superspace, spherical superfunction 
@article{DOCMA_2014__19__a1,
     author = {Alldridge, Alexander and Palzer, Wolfgang},
     title = {Asymptotics of spherical superfunctions on rank one {Riemannian} symmetric superspaces},
     journal = {Documenta mathematica},
     pages = {1317--1366},
     publisher = {mathdoc},
     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a1/}
}
TY  - JOUR
AU  - Alldridge, Alexander
AU  - Palzer, Wolfgang
TI  - Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces
JO  - Documenta mathematica
PY  - 2014
SP  - 1317
EP  - 1366
VL  - 19
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a1/
LA  - en
ID  - DOCMA_2014__19__a1
ER  - 
%0 Journal Article
%A Alldridge, Alexander
%A Palzer, Wolfgang
%T Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces
%J Documenta mathematica
%D 2014
%P 1317-1366
%V 19
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a1/
%G en
%F DOCMA_2014__19__a1
Alldridge, Alexander; Palzer, Wolfgang. Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces. Documenta mathematica, Tome 19 (2014), pp. 1317-1366. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a1/