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Weyl modules for Lie superalgebras


Authors: Lucas Calixto, Joel Lemay and Alistair Savage
Journal: Proc. Amer. Math. Soc. 147 (2019), 3191-3207
MSC (2010): Primary 17B65, 17B10
DOI: https://doi.org/10.1090/proc/13146
Published electronically: April 18, 2019
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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.


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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

DOI: https://doi.org/10.1090/proc/13146
Keywords: Lie superalgebra, basic Lie superalgebra, Weyl module, Kac module, tensor product.
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
Article copyright: © 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.