Vogan has conjectured that a family of cohomologically induced modules exhaust the unitary dual of U(p, q) for certain kinds of integral infinitesimal characters. In this expository note (which is substantially a transcript of a talk given at the 1997 Seattle conference on the representation theory of real and p-adic groups) we recall the definition of the relevant modules, describe an approach...

We study the Wakimoto modules over the affine Kac-Moody algebras at the critical level from the point of view of the equivalences of categories proposed in our previous works, relating categories of representations and certain categories of sheaves. In particular, we describe explicitly geometric realizations of the Wakimoto modules as Hecke eigen-Dmodules on the affine Grassmannian and as quas...

We classify contravariant pairings between standard Whittaker modules and Verma over a complex semisimple Lie algebra. These are useful in extending several classical techniques for category O to the Miličić–Soergel N. introduce class of costandard which generalize dual modules, describe canonical maps from terms pairings. show that have unique irreducible submodules share same composition fact...

Dual-Vth design is an effective leakage power reduction technique at behavioral synthesis level. It allows designers to replace modules on non-critical path with the highVth implementation. However, the existing constructive algorithms fail to find the optimal solution due to the complexity of the problem and do not consider the on-chip temperature variation. In this paper, we propose a two-sta...

Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

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.

For W*-algebras A and self-dual Hilbert A-modules M we show that every selfadjoint, ”compact” module operator on M is diagonalizable. Some specific properties of the eigenvalues and of the eigenvectors are described.

An elementary proof is given for Hutchinson’s duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.

Let $R\ $be a commutative ring with $1\neq0$ and $M$ be an $R$-module. Suppose that $S\subseteq R\ $is multiplicatively closed set of $R.\ $Recently Sevim et al. in \cite{SenArTeKo} introduced the notion $S$-prime submodule which is generalization prime used them to characterize certain classes rings/modules such as submodules, simple modules, torsion free modules,\ $S$-Noetherian modules etc. ...

We establish a formula for the weight multiplicities of Demazure modules (in particular for highest weight representations) of a complex connected algebraic group in terms of the geometry of its Langlands dual.