KAZHDAN-LUSZTIG-POLYNOME UND UNZERLEGBARE BIMODULN ÜBER POLYNOMRINGEN

@article{Soergel2004KAZHDANLUSZTIGPOLYNOMEUU,
  title={KAZHDAN-LUSZTIG-POLYNOME UND UNZERLEGBARE BIMODULN {\"U}BER POLYNOMRINGEN},
  author={Wolfgang Soergel},
  journal={Journal of the Institute of Mathematics of Jussieu},
  year={2004},
  volume={6},
  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. 
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175 Citations
Highly Influential Citations
13
Background Citations
39
Methods Citations
20
Results Citations
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175 Citations

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References

SHOWING 1-10 OF 14 REFERENCES

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…

On the relation between intersection cohomology and representation theory in positive characteristic

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.…

The combinatorics of Harish-Chandra bimodules.

On some generalisations of the Kazhdan-Lusztig polynomials for “universal” Coxeter systems

Cells in Affine Weyl Groups

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