Representation theoretic embedding of twisted Dirac operators
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- by S. Mehdi and P. Pandžić
- Represent. Theory 25 (2021), 760-779
- DOI: https://doi.org/10.1090/ert/583
- Published electronically: September 20, 2021
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Abstract:
Let $G$ be a non-compact connected semisimple real Lie group with finite center. Suppose $L$ is a non-compact connected closed subgroup of $G$ acting transitively on a symmetric space $G/H$ such that $L\cap H$ is compact. We study the action on $L/L\cap H$ of a Dirac operator $D_{G/H}(E)$ acting on sections of an $E$-twist of the spin bundle over $G/H$. As a byproduct, in the case of $(G,H,L)=(SL(2,{\mathbb R})\times SL(2,{\mathbb R}),\Delta (SL(2,{\mathbb R})\times SL(2,{\mathbb R})),SL(2,{\mathbb R})\times SO(2))$, we identify certain representations of $L$ which lie in the kernel of $D_{G/H}(E)$.References
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Bibliographic Information
- S. Mehdi
- Affiliation: Institut Elie Cartan de Lorraine, CNRS - UMR 7502, Université de Lorraine, France
- MR Author ID: 609901
- Email: salah.mehdi@univ-lorraine.fr
- P. Pandžić
- Affiliation: Department of Mathematics, Faculty of Science, University of Zagreb, Croatia
- ORCID: 0000-0002-7405-4381
- Email: pandzic@math.hr
- Received by editor(s): February 6, 2021
- Received by editor(s) in revised form: June 6, 2021
- Published electronically: September 20, 2021
- Additional Notes: The second author was supported by the QuantiXLie Center of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme (KK.01.1.1.01.0004)
- © Copyright 2021 American Mathematical Society
- Journal: Represent. Theory 25 (2021), 760-779
- MSC (2020): Primary 22E46; Secondary 43A85
- DOI: https://doi.org/10.1090/ert/583
- MathSciNet review: 4315588