author={Wolfgang Soergel},
  journal={Journal of the Institute of Mathematics of Jussieu},
  pages={501 - 525}
  • W. Soergel
  • Published 29 March 2004
  • Mathematics
  • Journal of the Institute of Mathematics of Jussieu
Wir entwickeln eine Strategie zum Beweis der Positivität der Koeffizienten von Kazhdan-Lusztig-Polynomen für beliebige Coxeter-Gruppen. We develop a strategy to prove the positivity of coefficients of Kazhdan–Lusztig polynomials for arbitrary Coxeter groups. 

Relative hard Lefschetz for Soergel bimodules

We prove the relative hard Lefschetz theorem for Soergel bimodules. It follows that the structure constants of the Kazhdan-Lusztig basis are unimodal. We explain why the relative hard Lefschetz

Kazhdan–Lusztig Conjectures and Shadows of Hodge Theory

We give an informal introduction to the authors’ work on some conjectures of Kazhdan and Lusztig, building on work of Soergel and de Cataldo–Migliorini. This article is an expanded version of a

The Hodge Theory of Soergel Bimodules

We prove Soergel’s conjecture on the characters of indecomposable Soergel bimodules. We deduce that Kazhdan-Lusztig polynomials have positive coecients for arbitrary Coxeter systems. Using results of

Modular Koszul duality for Soergel bimodules

We generalize the modular Koszul duality of Achar-Riche to the setting of Soergel bimodules associated to any finite Coxeter system. The key new tools are a functorial monodromy action and

Categorification of a Recursive Formula for Kazhdan–Lusztig Polynomials

We obtain explicit branching rules for graded cell modules and graded simple modules over the endomorphism algebra of a Bott–Samelson bimodule. These rules allow us to categorify a well-known

Soergel bimodules for universal Coxeter groups

We produce an explicit recursive formula which computes the idempotent projecting to any indecomposable Soergel bimodule for a universal Coxeter system. This gives the exact set of primes for which

Jucys-Murphy operators for Soergel bimodules

We produce Jucys-Murphy elements for the diagrammatical category of Soergel bimodules associated with general Coxeter groups, and use them to diagonalize the bilinear form on the cell modules. This


The monoidal category of Soergel bimodules is an incarnation of the Hecke category and plays a fundamental role in Kazhdan-Lusztig theory. We present this category by generators and relations, using



Representations of Coxeter groups and Hecke algebras

here l(w) is the length of w. In the case where Wis a Weyl group and q is specialized to a fixed prime power, | ~ can be interpreted as the algebra of intertwining operators of the space of functions

From moment graphs to intersection cohomology

Abstract. We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero- and

Reflection groups and coxeter groups

Part I. Finite and Affine Reflection Groups: 1. Finite reflection groups 2. Classification of finite reflection groups 3. Polynomial invariants of finite reflection groups 4. Affine reflection groups

Infinite-dimensional Lie algebras

1. Basic concepts.- 1. Preliminaries.- 2. Nilpotency and solubility.- 3. Subideals.- 4. Derivations.- 5. Classes and closure operations.- 6. Representations and modules.- 7. Chain conditions.- 8.

Untersuchungen zu den Kazhdan-Lusztig-Polynomen und zu dazupassenden Bimoduln

  • Diplomarbeit in Freiburg
  • 1999

und die Topologie der Fahnenmannigfaltigkeit einer Kac-Moody-Gruppe

  • Dissertation in Freiburg
  • 1999