PreprintarXiv licencearXiv
Symmetric spaces and skew multiplicity free representations
Abstract
Let $ G $ be a non-compact connected reductive real Lie group and $ P $ its parabolic subgroup. We give a list of equivalent conditions for $ P $ to have an abelian unipotent radical. These conditions are related to skew multiplicity free and multiplicity free actions, and using the theory of Clifford algebra and the cubic Dirac operator we deduce formulas for the de Rham cohomology of compact symmetric spaces $ G/P $.
Related
- Multiplicity One and van Dijk's Conjecture for Connected Complex Symmetric Spaces
- On skew-symmetric distributions and their use in Monte Carlo sampling algorithms: coordinate-free, Gibbs-style and manifold versions of the Barker proposal
- Generic distinction of induced representations: the case of symmetric spaces
- The symmetric skew monoidal structure of Gray-categories
- Lie nilpotency index of skew symmetric elements in group algebras
BibTeX
@misc{calvert2026symmetric,
title = {{Symmetric spaces and skew multiplicity free representations}},
author = {Kieran Calvert and Kyo Nishiyama and Pavle Pandžić},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38507},
eprint = {2609.38507},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38507},
}
RIS
TY - UNPB
TI - Symmetric spaces and skew multiplicity free representations
AU - Kieran Calvert
AU - Kyo Nishiyama
AU - Pavle Pandžić
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38507
UR - https://arxiv.org/abs/2609.38507
AB - Let $ G $ be a non-compact connected reductive real Lie group and $ P $ its parabolic subgroup. We give a list of equivalent conditions for $ P $ to have an abelian unipotent radical. These conditions are related to skew multiplicity free and multiplicity free actions, and using the theory of Clifford algebra and the cubic Dirac operator we deduce formulas for the de Rham cohomology of compact symmetric spaces $ G/P $.
ER -