Weyl modules for Lie superalgebras
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- by Lucas Calixto, Joel Lemay and Alistair Savage PDF
- Proc. Amer. Math. Soc. 147 (2019), 3191-3207
Abstract:
We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak {g} \otimes A$, where $A$ is an associative commutative unital $\mathbb {C}$-algebra and $\mathfrak {g}$ is a basic Lie superalgebra or $\mathfrak {sl}(n,n)$, $n \ge 2$. Under some mild assumptions, we prove universality, finite-dimensionality, and tensor product decomposition properties for these modules. These properties are analogues of those of Weyl modules in the non-super setting. We also point out some features that are new in the super case.References
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Additional Information
- Lucas Calixto
- Affiliation: UNICAMP-IMECC, Campinas - SP - Brazil, 13083-859
- Address at time of publication: Department of Mathematics, Federal University of Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
- Email: lhcalixto@ufmg.br
- Joel Lemay
- Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada
- Email: jlema072@uottawa.ca
- Alistair Savage
- Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada
- Email: alistair.savage@uottawa.ca
- Received by editor(s): June 2, 2015
- Received by editor(s) in revised form: February 8, 2016
- Published electronically: April 18, 2019
- Additional Notes: The first author was supported by FAPESP grant 2013/08430-4. The second author was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Postgraduate Scholarship. The third author was supported by an NSERC Discovery Grant.
- Communicated by: Kailash Misra
- © Copyright 2019 Copyright by the authors. Permission is granted to copy for educational and scientific purposes. This work is dedicated to the public domain after 28 years from the date of publication.
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3191-3207
- MSC (2010): Primary 17B65, 17B10
- DOI: https://doi.org/10.1090/proc/13146
- MathSciNet review: 3981101