We construct a duality functor on the category of continuous representations linearly compact Lie superalgebras, using representation theory conformal superalgebras. compute dual generalized Verma modules.

The motivation for this paper goes back to at least the work of A. Borel, R. Bott and A. Weil on their geometric construction of irreducible representations of complex simple Lie groups, and the related work of B. Kostant [10] and J. Bernšteı̆n, I. Gel′fand and S. Gel′fand [2]. Articles more closely related to ours are those of H. Jakobsen and V. Kac [9] and then presumably Wakimoto [11] and mor...

The main purpose of the paper is to establish new tools in study $\mathcal{O}^\mathfrak{p}$. We introduce Jantzen coefficients generalized Verma modules. It comes from Jantzen's simplicity criteria for modules and has a deep relation with structure develop reduction process compute those coefficients. For which we need consider induced maximal parabolic subalgebras having nontrivial singularity...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

The construction of causal graphs from non-experimental data rests on a set of constraints that the graph structure imposes on all probability distributions compatible with the graph. These constraints are of two types: conditional independencies and algebraic constraints, first noted by Verma. While conditional independencies are well studied and frequently used in causal induction algorithms,...

The Harish-Chandra homomorphism is due to [Harish-Chandra 1951]. Attention to universal modules with highest weights is in ]Harish-Chandra 1951], [Cartier 1955], as well as [Verma 1968], [BernsteinGelfand-Gelfand 1971a], [Bernstein-Gelfand-Gelfand 1971b], [Bernstein-Gelfand-Gelfand 1975]. See also [Jantzen 1979]. [1℄ We treat sl(2) in as simple a style as possible, to highlight ideas. Then sl(3...