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Transactions of the American Mathematical Society

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Dirac index and twisted characters


Authors: Dan Barbasch, Pavle Pandžić and Peter Trapa
Journal: Trans. Amer. Math. Soc. 371 (2019), 1701-1733
MSC (2010): Primary 22E46
DOI: https://doi.org/10.1090/tran/7318
Published electronically: October 26, 2018
MathSciNet review: 3894032
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Abstract: Let $ G$ be a real reductive Lie group with maximal compact subgroup $ K$. We generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in cases when $ G$ and $ K$ do not have equal rank. We compute ordinary and twisted indices of standard modules. As applications, we study extensions of Harish-Chandra modules and twisted characters.


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Additional Information

Dan Barbasch
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14850
Email: barbasch@math.cornell.edu

Pavle Pandžić
Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
Email: pandzic@math.hr

Peter Trapa
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: ptrapa@math.utah.edu

DOI: https://doi.org/10.1090/tran/7318
Received by editor(s): July 15, 2016
Received by editor(s) in revised form: June 27, 2017
Published electronically: October 26, 2018
Additional Notes: The first author was supported by NSA grant H98230-16-1-0006
The second author was supported by grant no. 4176 of the Croatian Science Foundation and 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)
Article copyright: © Copyright 2018 American Mathematical Society