Representation theory of N=2 super Virasoro algebra: twisted sector

In this article, we study the structure of Verma modules and Fock modules over the twisted sector of the N=2 super Virasoro algebras.     

与过程相联系的σ-代数流

讨化了σ-代数流的结构,并给出其一般性的结果;归纳出各σ-代数流的相互关系;最后介绍其两个简单应用.     

Filtrations of Simplicial Functors and the Novikov Conjecture

We show that the Strong Novikov Conjecture for the maximal C^*-algebra C^*(π) of a discrete group π is equivalent to a statement in topological K-theory for which the corresponding statement in algebraic K-theory is always true. We also show that for any group π, rational injectivity of the full assembly map for K_*^t(C^*(π)) follows from rational injectivity of the restricted assembly map. (Received: February 2006)     

Andersen Filtration and Hard Lefschetz

On the space of homomorphisms from a Verma module to an indecomposable tilting module of the BGG-category we define a natural filtration following Andersen [A] and establish a formula expressing the dimensions of the filtration steps in terms of coefficients of Kazhdan–Lusztig polynomials. Received: May 2006, Revision: July 2007, Accepted: July 2007     

Structure of T Modules and Restricted Duals: The Classical and the Quantum Case

Abstract

A concrete realization of Enright's T modules is obtained. This is used to show their self-duality. As a consequence, the restricted duals of Verma modules are also identified.     

Verma modules for twisted Yangians

Abstract

A sufficient and necessary condition for the reducibility of the Verma modules over the twisted Yangians of rank one is given.     

Submodule Structure of Generalized Verma Modules Induced from Generic Gelfand-Zetlin Modules

For complex Lie algebra sl(n, C) we study the submodule structure of generalized Verma modules induced from generic Gelfand-Zetlin modules over some subalgebra of type sl(k, C). We obtain necessary and sufficient conditions for the existence of a submodule generalizing the Bernstein-Gelfand-Gelfand theorem for Verma modules.     

Prime Filtrations and Primary Decompositions of Modules

We give a new characterization for prime filtrations of an R-module M in terms of primary decomposition of the zero submodule of M. Using this characterization we prove that some classes of monomial ideals like generic and cogeneric monomial ideals are clean, pretty clean, or almost clean.     

Verma-Type Modules for Quantum Affine Lie Algebras

Let be an untwisted affine Kac–Moody algebra and M_J() a Verma-type module for with J-highest weight P. We construct quantum Verma-type modules M_J^q() over the quantum group , investigate their properties and show that M_J^q() is a true quantum deformation of M_J() in the sense that the weight structure is preserved under the deformation. We also analyze the submodule structure of quantum Verma-type modules. Presented by A. VerschorenMathematics Subject Classifications (2000) 17B37, 17B67, 81R50.The first author is a Regular Associate of the ICTP. The third author was supported in part by a Faculty Research Grant from St. Lawrence University.     

A note on tilting sequences

We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.      

Fock Space Realizations of Imaginary Verma Modules

This work expands to the setting of the results of H. Jakobsen and V. Kac and independently D. Bernard and G. Felder on the realization of , in terms of infinite sums of partial differential operators. We note in the paper that, in the generic case, these geometric constructions are just realizations of the imaginary Verma modules studied by V. Futorny. Presented by A. VerschorenMathematics Subject Classifications (2000) Primary: 17B67, 81R10.     

Highest weight representations of a Lie algebra of Block type

For a field F of characteristic zero and an additive subgroup G of F, a Lie algebra B(G) of the Block type is defined with the basis {Lα,i, c|α∈G, -1≤i∈Z} and the relations [Lα,i,Lβ,j] = ((i 1)β- (j 1)α)Lα β,i j αδα,-βδi j,-2c,[c, Lα,i] = 0. Given a total order (?) on G compatible with its group structure, and anyα∈B(G)0*, a Verma B(G)-module M(A, (?)) is defined, and the irreducibility of M(A,(?)) is completely determined. Furthermore, it is proved that an irreducible highest weight B(Z )-module is quasifinite if and only if it is a proper quotient of a Verma module.     

Tilting Preenvelopes and Cotilting Precovers

We relate the theory of envelopes and covers to tilting and cotilting theory, for (infinitely generated) modules over arbitrary rings. Our main result characterizes tilting torsion classes as the pretorsion classes providing special preenvelopes for all modules. A dual characterization is proved for cotilting torsion-free classes using the new notion of a cofinendo module. We also construct unique representing modules for these classes.