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Spinoriality of orthogonal representations of reductive groups


Authors: Rohit Joshi and Steven Spallone
Journal: Represent. Theory 24 (2020), 435-469
MSC (2010): Primary 20G15; Secondary 22E46
DOI: https://doi.org/10.1090/ert/552
Published electronically: September 16, 2020
MathSciNet review: 4150223
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Abstract: Let $G$ be a connected reductive group over a field $F$ of characteristic $0$, and $\varphi : G \to \operatorname {SO}(V)$ an orthogonal representation over $F$. We give criteria to determine when $\varphi$ lifts to the double cover $\operatorname {Spin}(V)$.


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Additional Information

Rohit Joshi
Affiliation: Bhaskaracharya Pratishthana, 56/14, Erandavane, Damle Path, off Law College Road, Pune-411004, Maharashtra, India; and Indian Institute of Science Education and Research, Pune-411021, India
ORCID: 0000-0002-2471-2737
Email: rohitsj@students.iiserpune.ac.in, rohitsj2004@gmail.com

Steven Spallone
Affiliation: Indian Institute of Science Education and Research, Pune-411021, India
MR Author ID: 824479
Email: sspallone@gmail.com

Keywords: Reductive groups, orthogonal representations, Dynkin index, lifting criterion, Weyl dimension formula
Received by editor(s): October 31, 2018
Received by editor(s) in revised form: February 21, 2020
Published electronically: September 16, 2020
Additional Notes: This paper comes out of the first author’s Ph.D. thesis at IISER Pune, during which he was supported by an Institute Fellowship. Afterwards he was supported by a fellowship from Bhaskaracharya Pratishthan.
Article copyright: © Copyright 2020 American Mathematical Society