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Induced representations from the Heisenberg parabolic subgroup of SL(n+2,ℝ)
Abstract
The group G = SL(n+2,R) has a parabolic subgroup P = MAN whose unipotent radical is a Heisenberg group. We study representations induced from a character of P, and using the Lie algebra action on the space of K-finite vectors we find the points of reducibility and the complementary series. We identify solutions to the conformally invariant systems of differential operators as subrepresentations.
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BibTeX
@misc{haastrecht2026induced,
title = {{Induced representations from the Heisenberg parabolic subgroup of $SL(n+2,\mathbbR)$}},
author = {Robin van Haastrecht},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40102},
eprint = {2610.40102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40102},
}
RIS
TY - UNPB
TI - Induced representations from the Heisenberg parabolic subgroup of SL(n+2,ℝ)
AU - Robin van Haastrecht
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40102
UR - https://arxiv.org/abs/2610.40102
AB - The group G = SL(n+2,R) has a parabolic subgroup P = MAN whose unipotent radical is a Heisenberg group. We study representations induced from a character of P, and using the Lie algebra action on the space of K-finite vectors we find the points of reducibility and the complementary series. We identify solutions to the conformally invariant systems of differential operators as subrepresentations.
ER -