Abstract
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 lecture given by the second author at the Arbeitstagung in memory of Frederich Hirzebruch.
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Notes
- 1.
Due, no doubt, to the influence which their work has had on the authors.
- 2.
Although all the R-modules will factor through R∕(R + W), we prefer the ring R for philosophical reasons. When W is infinite, the ring R∕(R + W) is infinite dimensional, as R W has the “wrong” transcendence degree, and the Chevalley theorem does not hold. The ring R behaves in a uniform way for all Coxeter groups, while the quotient ring R∕(R + W) does not.
- 3.
W. Soergel pointed out that this is a bad name, as it has nothing whatsoever to do with coinvariants.
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Elias, B., Williamson, G. (2016). Kazhdan–Lusztig Conjectures and Shadows of Hodge Theory. In: Ballmann, W., Blohmann, C., Faltings, G., Teichner, P., Zagier, D. (eds) Arbeitstagung Bonn 2013. Progress in Mathematics, vol 319. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-43648-7_5
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