An Explicit Plancherel Formula for Line Bundles over the One-Sheeted Hyperboloid
Journal of Lie Theory, Volume 33 (2023) no. 2, pp. 453-476
We consider $G=\rm SL(2,\mathbb{R})$ and $H$ the subgroup of diagonal matrices. Then $X=G/H$ is a unimodular homogeneous space which can be identified with the one-sheeted hyperboloid. For each unitary character $\chi$ of $H$ we decompose the induced representations $\rm Ind_H^G(\chi)$ into irreducible unitary representations, known as a Plancherel formula. This is done by studying explicit intertwining operators between $\rm Ind_H^G(\chi)$ and principal series representations of $G$. These operators depends holomorphically on the induction parameters.
@article{JOLT_2023_33_2_a0,
author = {F. Bang-Jensen and J. Ditlevsen},
title = {An {Explicit} {Plancherel} {Formula} for {Line} {Bundles} over the {One-Sheeted} {Hyperboloid
}},
journal = {Journal of Lie Theory},
pages = {453--476},
year = {2023},
volume = {33},
number = {2},
doi = {10.5802/jolt.1290},
zbl = {1542.22021},
language = {en},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1290/}
}
TY - JOUR AU - F. Bang-Jensen AU - J. Ditlevsen TI - An Explicit Plancherel Formula for Line Bundles over the One-Sheeted Hyperboloid JO - Journal of Lie Theory PY - 2023 SP - 453 EP - 476 VL - 33 IS - 2 UR - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1290/ DO - 10.5802/jolt.1290 LA - en ID - JOLT_2023_33_2_a0 ER -
%0 Journal Article %A F. Bang-Jensen %A J. Ditlevsen %T An Explicit Plancherel Formula for Line Bundles over the One-Sheeted Hyperboloid %J Journal of Lie Theory %D 2023 %P 453-476 %V 33 %N 2 %U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1290/ %R 10.5802/jolt.1290 %G en %F JOLT_2023_33_2_a0
F. Bang-Jensen; J. Ditlevsen. An Explicit Plancherel Formula for Line Bundles over the One-Sheeted Hyperboloid. Journal of Lie Theory, Volume 33 (2023) no. 2, pp. 453-476. doi: 10.5802/jolt.1290
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