Weyl modules for Lie superalgebras

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.

15 pages. v2: Minor corrections, published version. v3: Correction to Definition 4.7 and Remark 4.8

References in corpus (5)

• On the center of quiver-Hecke algebras
• Representations of Quantum Affine Superalgebras
• Current algebras and categorified quantum groups
• Global Weyl modules for equivariant map algebras
• Equivariant map queer Lie superalgebras

Cited by in corpus (1)

• Completeness of Bethe ansatz for Gaudin models associated with gl(1|1)