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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)

- FÜR KIPP-MODULN, WOLFGANG SOERGEL, Corinne Blondel, Michèle Couillens, Jens Carsten Jantzen, Friedrich Knop
- 1997

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)

- WOLFGANG SOERGEL, Corinne Blondel, Michèle Couillens, Caroline Gruson, Jens Carsten Jantzen, Friedrich Knop
- 1997

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.

- Robert W. Bauml, Wolfgang Sörgel
- 2008 16th European Signal Processing Conference
- 2008

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)

- Dragan Mili, Wolfgang Soergel
- 1995

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.

- WOLFGANG SOERGEL
- 1998

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)

Let Λ be a left and right Artin ring and ΛωΛ a faithfully balanced selforthogonal bimodule. We give a sufficient condition that the injective dimension of ωΛ is finite implies that of Λω is also finite. 2003 Elsevier Science (USA). All rights reserved.

- Alexander Schasse, Timo Gerkmann, Rainer Martin, Wolfgang Sörgel, Thomas Pilgrim, Henning Puder
- IEEE/ACM Transactions on Audio, Speech, and…
- 2015

The filter-bank system implemented in hearing aids has to fulfill various constraints such as low latency and high stop-band attenuation, usually at the cost of low frequency resolution. In the context of frequency-domain noise-reduction algorithms, insufficient frequency resolution may lead to annoying residual noise artifacts since the spectral harmonics… (More)