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We determine the Verma multiplicities and the characters of projective modules for atypical blocks in the BGG Category O for the general linear Lie superalgebras $frak{gl}(2|2)$ and $frak{gl}(3|1)$. We then explicitly determine the composition factor multiplcities of Verma modules in the atypicality 2 block of $frak{gl}(2|2)$.
We determine the Verma multiplicities of standard filtrations of projective modules for integral atypical blocks in the BGG category $mathcal{O}$ for the orthosymplectic Lie superalgebras $mathfrak{osp}(3|4)$ by way of translation functors. We then e
The main goal of this paper is to show that a wide variety of infinite-dimensional algebras all share a common structure, including a triangular decomposition and a theory of weights. This structure allows us to define and study the BGG Category O, g
We construct a Bernstein-Gelfand-Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra. As a consequence it follows that the unique maximal subm
This article aims to contribute to the study of algebras with triangular decomposition over a Hopf algebra, as well as the BGG Category O. We study functorial properties of O across various setups. The first setup is over a skew group ring, involving
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