Journal of Lie Theory

no. 1
On Some Degenerate Principal Series Representations of O(p,2)
Journal of Lie Theory, Volume 11 (2001) no. 1, pp. 23-55
We consider representations of O(p, 2)  (p>4)  induced from one-dimensional representations of a maximal parabolic subgroup. We first decompose them into K-types using Stiefel harmonics theory, then write down the actions of the noncompact part. Now the reducibility and the unitarizability of the irreducible constituents are deduced.
DOI: 10.5802/jolt.221
Classification: 22E46
Keywords: semisimple Lie groups, induced representations, maximal parabolic subgroups, \(K\)-types, pseudo-orthogonal group, harmonic analysis, hyperboloids, Stiefel manifold 
@article{JOLT_2001_11_1_a2,
     author = {T. Fujimura},
     title = {On {Some} {Degenerate} {Principal} {Series} {Representations} of {O(p,2)}},
     journal = {Journal of Lie Theory},
     pages = {23--55},
     year = {2001},
     volume = {11},
     number = {1},
     doi = {10.5802/jolt.221},
     zbl = {0972.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.221/}
}
TY  - JOUR
AU  - T. Fujimura
TI  - On Some Degenerate Principal Series Representations of O(p,2)
JO  - Journal of Lie Theory
PY  - 2001
SP  - 23
EP  - 55
VL  - 11
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.221/
DO  - 10.5802/jolt.221
ID  - JOLT_2001_11_1_a2
ER  - 
%0 Journal Article
%A T. Fujimura
%T On Some Degenerate Principal Series Representations of O(p,2)
%J Journal of Lie Theory
%D 2001
%P 23-55
%V 11
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.221/
%R 10.5802/jolt.221
%F JOLT_2001_11_1_a2
T. Fujimura. On Some Degenerate Principal Series Representations of O(p,2). Journal of Lie Theory, Volume 11 (2001) no. 1, pp. 23-55. doi: 10.5802/jolt.221

Cited by Sources: