Geodesic
The Plancherel Formula for Minimal Parabolic Subgroups
Journal of Lie theory, Tome 24 (2014) no. 3, pp. 791-808.

Voir la notice de l'article provenant de la source Heldermann Verlag

In a recent paper we found conditions for a nilpotent Lie group to be foliated into subgroups that have square integrable unitary representations that fit together to form a filtration by normal subgroups. That resulted in explicit character formulae, Plancherel Formulae and multiplicity formulae. We also showed that nilradicals N of minimal parabolic subgroups P = MAN enjoy that "stepwise square integrable" property. Here we extend those results from N to P. The Pfaffian polynomials, which give orthogonality relations and Plancherel density for N, also give a semi-invariant differential operator that compensates lack of unimodularity for P. The result is a completely explicit Plancherel Formula for $P$.
Classification : 22E, 43A, 52C
Mots-clés : Lie group, Plancherel formula, Fourier inversion, parabolic subgroup, Dixmier-Pukanszky operator, square integrable representation, stepwise square integrable representation 
@article{JLT_2014_24_3_JLT_2014_24_3_a9,
     author = {J. A. Wolf },
     title = {The {Plancherel} {Formula} for {Minimal} {Parabolic} {Subgroups}},
     journal = {Journal of Lie theory},
     pages = {791--808},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a9/}
}
TY  - JOUR
AU  - J. A. Wolf 
TI  - The Plancherel Formula for Minimal Parabolic Subgroups
JO  - Journal of Lie theory
PY  - 2014
SP  - 791
EP  - 808
VL  - 24
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a9/
ID  - JLT_2014_24_3_JLT_2014_24_3_a9
ER  - 
%0 Journal Article
%A J. A. Wolf 
%T The Plancherel Formula for Minimal Parabolic Subgroups
%J Journal of Lie theory
%D 2014
%P 791-808
%V 24
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a9/
%F JLT_2014_24_3_JLT_2014_24_3_a9
J. A. Wolf . The Plancherel Formula for Minimal Parabolic Subgroups. Journal of Lie theory, Tome 24 (2014) no. 3, pp. 791-808. http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a9/