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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Representation theoretic embedding of twisted Dirac operators
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by S. Mehdi and P. Pandžić PDF
Represent. Theory 25 (2021), 760-779 Request permission

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 $D_{G/H}(E)$.
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Additional 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