Filtration de certains espaces de fonctions sur un espace symétrique réductif
Delorme, Patrick ; Souaifi, Sofiane
HAL, hal-00089062 / Harvested from HAL
Text on HAL
We introduce a filtration of a (g.K)-module of some space of functions on a reductive symmetric space G/H, and compute the associated grading as a direct sum of induced representations. As an application of this result to the reductive groups viewed as symmetric spaces, we are able to realize any Harish-Chandra module as a subquotient of a direct sum of induced representations from parabolic subgroups, the inducing representations being trivial on the unipotent radical.
Publié le : 2004-07-05
Classification:  Reductive symmetric spaces,  Invariant differential operators,  Eigenfunctions,  Generalized principal series,  Harish-Chandra modules,  Sub-quotient theorem,  [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 
@article{hal-00089062,
     author = {Delorme, Patrick and Souaifi, Sofiane},
     title = {Filtration de certains espaces de fonctions sur un espace sym\'etrique r\'eductif},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/hal-00089062}
}

Delorme, Patrick; Souaifi, Sofiane. Filtration de certains espaces de fonctions sur un espace symétrique réductif. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00089062/