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We classify all simple bounded highest weight modules of a basic classical Lie superalgebra $mathfrak g$. In particular, our classification leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongly typical bounded highest weight modules of $mathfrak g$.
In this paper, a family of non-weight modules over Lie superalgebras $S(q)$ of Block type are studied. Free $U(eta)$-modules of rank $1$ over Ramond-Block algebras and free $U(mathfrak{h})$-modules of rank $2$ over Neveu-Schwarz-Block algebras are co
We prove that the tensor product of a simple and a finite dimensional $mathfrak{sl}_n$-module has finite type socle. This is applied to reduce classification of simple $mathfrak{q}(n)$-supermodules to that of simple $mathfrak{sl}_n$-modules. Rough st
In this paper the authors introduce a class of parabolic subalgebras for classical simple Lie superalgebras associated to the detecting subalgebras introduced by Boe, Kujawa and Nakano. These parabolic subalgebras are shown to have good cohomological
In 2006, Gao and Zeng cite{GZ} gave the free field realizations of highest weight modules over a class of extended affine Lie algebras. In the present paper, applying the technique of localization to those free field realizations, we construct a clas
Let ${mathcal W}_n$ be the Lie algebra of polynomial vector fields. We classify simple weight ${mathcal W}_n$-modules $M$ with finite weight multiplicities. We prove that every such nontrivial module $M$ is either a tensor module or the unique simple