New bases of some Hecke algebras via Soergel bimodules 

Advances in Math. 228 (2011) 1043-1067. This is a first attempt to find explicitly Soergel indecomposable bimodules for extra-large Coxeter systems. This is very linked with my "Forking path conjecture" (see the paper "Gentle Introduction to Soergel bimodules" above), an extremely strange phenomenon that I would love to understand better.

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