Square Integrable Representations of Reductive Lie Groups with Admissible Restriction to SL2(R)
Journal of Lie theory, Tome 27 (2017) no. 4, pp. 1033-1056
We determine the irreducible square integrable representations of a reductive connected Lie group which admit an H-admissible restriction to a subgroup H locally isomorphic to SL2(R). We show that such a representation is holomorphic and we determine the essentially unique H with this property as well as multiplicity formulae.
Classification :
22E46, 17B10
Mots-clés : Discrete Series, branching laws, admissible restriction
Mots-clés : Discrete Series, branching laws, admissible restriction
@article{JLT_2017_27_4_JLT_2017_27_4_a7,
author = {M. Duflo and E. Galina and J. A. Vargas},
title = {Square {Integrable} {Representations} of {Reductive} {Lie} {Groups} with {Admissible} {Restriction} to {SL\protect\textsubscript{2}(R)}},
journal = {Journal of Lie theory},
pages = {1033--1056},
year = {2017},
volume = {27},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a7/}
}
TY - JOUR AU - M. Duflo AU - E. Galina AU - J. A. Vargas TI - Square Integrable Representations of Reductive Lie Groups with Admissible Restriction to SL2(R) JO - Journal of Lie theory PY - 2017 SP - 1033 EP - 1056 VL - 27 IS - 4 UR - http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a7/ ID - JLT_2017_27_4_JLT_2017_27_4_a7 ER -
%0 Journal Article %A M. Duflo %A E. Galina %A J. A. Vargas %T Square Integrable Representations of Reductive Lie Groups with Admissible Restriction to SL2(R) %J Journal of Lie theory %D 2017 %P 1033-1056 %V 27 %N 4 %U http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a7/ %F JLT_2017_27_4_JLT_2017_27_4_a7
M. Duflo; E. Galina; J. A. Vargas. Square Integrable Representations of Reductive Lie Groups with Admissible Restriction to SL2(R). Journal of Lie theory, Tome 27 (2017) no. 4, pp. 1033-1056. http://geodesic.mathdoc.fr/item/JLT_2017_27_4_JLT_2017_27_4_a7/