1Dép. de Mathématiques, Faculté de Sciences, 3038 Sfax, Tunisia 2Dept. of Mathematics and Computer Science, University of Missouri, St. Louis, MO 63121, U.S.A. 3Let G be a connected and simply connected nilpotent Lie group with Lie algebra L(G) and unitary dual D(G). The moment map for π of D(G) sends smooth vectors in the representation space of π to L(G) 4. The closure of the image of the moment map for π is called its 5. N. Wildberger has proved that the moment set for π coincides with the closure of the convex hull of the corresponding coadjoint orbit. We say that D(G) is 6when the moment sets differ for any pair of distinct irreducible unitary representations. Our main results provide sufficient and necessary conditions for moment separability in a restricted class of nilpotent groups. 7[
Journal of Lie Theory, Tome 11 (2001) no. 1, pp. 135-154
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Ali Baklouti; Chal Benson; Gail Ratcliff. Moment Sets and the Unitary Dual of a Nilpotent Lie Group. Journal of Lie Theory, Tome 11 (2001) no. 1, pp. 135-154. http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a7/
@article{JOLT_2001_11_1_a7,
author = {Ali Baklouti and Chal Benson and Gail Ratcliff},
title = {Moment {Sets} and the {Unitary} {Dual} of a {Nilpotent} {Lie} {Group}},
journal = {Journal of Lie Theory},
pages = {135--154},
year = {2001},
volume = {11},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a7/}
}
TY - JOUR
AU - Ali Baklouti
AU - Chal Benson
AU - Gail Ratcliff
TI - Moment Sets and the Unitary Dual of a Nilpotent Lie Group
JO - Journal of Lie Theory
PY - 2001
SP - 135
EP - 154
VL - 11
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a7/
ID - JOLT_2001_11_1_a7
ER -
%0 Journal Article
%A Ali Baklouti
%A Chal Benson
%A Gail Ratcliff
%T Moment Sets and the Unitary Dual of a Nilpotent Lie Group
%J Journal of Lie Theory
%D 2001
%P 135-154
%V 11
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2001_11_1_a7/
%F JOLT_2001_11_1_a7
Let G be a connected and simply connected nilpotent Lie group with Lie algebra L(G) and unitary dual D(G). The moment map for π of D(G) sends smooth vectors in the representation space of π to L(G)*. The closure of the image of the moment map for π is called its moment set. N. Wildberger has proved that the moment set for π coincides with the closure of the convex hull of the corresponding coadjoint orbit. We say that D(G) is moment separable when the moment sets differ for any pair of distinct irreducible unitary representations. Our main results provide sufficient and necessary conditions for moment separability in a restricted class of nilpotent groups.
