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The aim of this paper is to work out a concrete example as well<lb>as to provide the general pattern of applications of Koszul duality to repre-<lb>sentation theory. The paper consists of three parts relatively independent of<lb>each other.<lb>The first part gives a reasonably selfcontained introduction to Koszul rings<lb>and Koszul duality. Koszul rings… (More)
Preface Lévy processes are an excellent tool for modelling price processes in mathematical finance. On the one hand, they are very flexible, since for any time increment ∆t any infinitely divisible distribution can be chosen as the increment distribution over periods of time ∆t. On the other hand, they have a simple structure in comparison with general… (More)
This article gives a selfcontained treatment of the theory of Kazhdan-Lusztig polynomials with special emphasis on affine reflection groups. There are only a few new results but several new proofs. We close with a conjectural character formula for tilting modules, which formed the starting point of these investigations.
We show how to express the characters of tilting modules in a (possibly parabolic) category O over a Kac-Moody algebra in terms of the characters of simple highest weight modules. This settles in lots of cases Conjecture 7.2 in Kazhdan-Lusztig-Polynome und eine Kombinatorik für KippModuln, Represent. Theory (1997), by the author, describing the character of… (More)
This article gives a self-contained treatment of the theory of Kazhdan-Lusztig polynomials with special emphasis on affine reflection groups. There are only a few new results but several new proofs. We close with a conjectural character formula for tilting modules, which formed the starting point of these investigations.
Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded t-structures with length heart and (4) bounded co-t-structures. These correspondences are shown to commute with mutations and partial orders. The results are valid for finite-dimensional algebras. A concrete example is given to illustrate how… (More)
Signal processing in hearing aids for purposes such as hearing loss compensation or noise reduction requires transforming the input signal into frequency bands. Additional audiological constraints need to be considered to accurately model the hearing loss compensation as well as to prevent unintended artefacts. This necessitates highly efficient solutions… (More)
Let G be a reductive algebraic group, with nilpotent cone N and flag variety B. We construct an exact functor from perverse sheaves on N to locally constant sheaves on B, and we use it to study Ext-groups and stalks of simple perverse sheaves on N in terms of the cohomology of B. 2010 Mathematics Subject Classification: Primary 20G05; Secondary 14F05, 32S60.
In this paper we develop a geometric approach to the study of the category of Whittaker modules. As an application, we reprove a wellknown result of B. Kostant on the structure of the category of non-degenerate Whittaker modules.
We show how to express the characters of tilting modules in a (possibly parabolic) category O over a Kac-Moody algebra in terms of the characters of simple highest weight modules. This settles, in lots of cases, Conjecture 7.2 of Kazhdan-Lusztig-Polynome and eine Kombinatorik für Kipp-Moduln, Representation Theory (An electronic Journal of the AMS) (1997),… (More)