Geodesic
Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces
Documenta mathematica, Tome 19 (2014), pp. 1317-1366
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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.
DOI : 10.4171/dm/482
Classification : 17B15, 22E45, 58A50
Mots-clés : Riemannian symmetric superspace, harish-chandra c-function, Lie supergroup, spherical superfunction 
@article{10_4171_dm_482,
     author = {Wolfgang Palzer and Alexander Alldridge},
     title = {Asymptotics of spherical superfunctions on rank one {Riemannian} symmetric superspaces},
     journal = {Documenta mathematica},
     pages = {1317--1366},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/482},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/482/}
}
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Wolfgang Palzer; Alexander Alldridge. Asymptotics of spherical superfunctions on rank one Riemannian symmetric superspaces. Documenta mathematica, Tome 19 (2014), pp. 1317-1366. doi: 10.4171/dm/482

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