Weyl modules for queer Lie superalgebras

Abstract

We define global and local Weyl modules for $q\otimes A$, where $q$ is the queer Lie superalgebra and A is an associative commutative unital $C$-algebra. We prove that global Weyl modules are universal highest weight objects in certain category up to parity reversing functor Π. Then with the assumption that A is finitely generated, it is shown that the local Weyl modules are finite dimensional and further they are universal highest map-weight objects in certain category up to Π. Finally, we prove a tensor product property for local Weyl modules.