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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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Spinoriality of orthogonal representations of reductive groups
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by Rohit Joshi and Steven Spallone PDF
Represent. Theory 24 (2020), 435-469 Request permission

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
  • 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.
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 435-469
  • MSC (2010): Primary 20G15; Secondary 22E46
  • DOI: https://doi.org/10.1090/ert/552
  • MathSciNet review: 4150223