Weyl modules for Lie superalgebras

Calixto, Lucas; Lemay, Joel; Savage, Alistair

doi:10.1090/proc/13146

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.

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