Related papers: Generalized Verma modules over sl(m+1) induced fro…

Let $M$ be G-graded R-module. The idea of a graded weakly primal submodule of $M$, which is a generalization of a graded primal submodule, is introduced and discussed in this paper. Some characteristics and characterizations are assigned to…

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…

Two classes of irreducible highest weight modules of the general linear Lie superalgebra $gl(1/\infty)$ are constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the algebra…

It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…

Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of regular functions on…

In this paper we classify degenerate Verma modules over the linearly compact Lie superalgebra $E(4,4)$. This completes the description of Verma modules over the exceptional linearly compact Lie superalgebras. As in the other cases all…

We formulate several basic properties of Verma supermodules over regular symmetrizable Kac--Moody Lie superalgebras, exhibiting $\mathfrak{gl}(1|1)$-nature as revealed through changing Borel subalgebras. We investigate variants of Verma…

Let $R$ be a ring with unity, $\sigma$ an endomorphism of $R$ and $M_R$ a right $R$-module. In this paper, we continue studding $\sigma$-rigid modules that were introduced by Gunner et al. \cite{generalized/rigid}. We give some results on…

We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…

For a tensor ring $T_R(M)$, we obtain sufficient and necessary conditions to describe all complete projective resolutions and all Gorenstein projective modules. As a consequence, we provide a method for constructing Gorenstein projective…

We classify semisimple module categories over the tensor category of representations of quantum SL(2) extending previous results to the roots of unity and positive characteristic cases.

Let B be the Lie algebra with basis {L_{i,j},C|i,j\in Z} and relations [L_{i,j},L_{k,l}]=((j+1)k-i(l+1))L_{i+k,j+l}+i\delta_{i,-k}\delta_{j+l,-2}C, [C,L_{i,j}]=0. It is proved that an irreducible highest weight B-module is quasifinite if…

The Verma modules over the quantum groups $\mathrm U_q(\mathfrak{gl}_{l + 1})$ for arbitrary values of $l$ are analysed. The explicit expressions for the action of the generators on the elements of the natural basis are obtained. The…

All simple weight modules with finite dimensional weight spaces over affine Lie algebras are classified.

In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

For any triple $(\mu,\lambda,\alpha)$ of complex numbers and an $\mathfrak a$-module ${V}$, a class of non-weight modules $\mathcal{M}\big(V,\mu,\Omega(\lambda,\alpha)\big)$ over the Virasoro algebra $\mathcal L$ is constructed in this…

We provide an explicit combinatorial description of highest weights of simple highest weight modules over the simple affine vertex algebra of type A of admissible level k. For admissible simple highest weight modules corresponding to the…

Using the tensor identity, we obtain decomposition results for the tensor product of a generalized Verma module with a module $M$ in the category $\mathcal{O}^{\mathfrak{p}}$, based on the decomposition of the restriction of $M$ to the…

Many properties of simple finite dimensional gl(m|n)-modules may be better understood by assigning weight diagrams to the highest weights with respect to a given base of simple roots. In this paper we consider bases that are compatible with…