2009/06/30 by Libedinsky, Nicolas
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.0907.0031
For extra-large Coxeter systems (m(s,r)>3), we construct a natural and explicit set of Soergel bimodules D=Dww∈ W such that each Dw contains as a direct summand (or is equal to) the indecomposable Soergel bimodule Bw. When decategorified, we prove that D gives rise to a set dww∈ W that is actually a basis of the Hecke algebra. This basis is close to the Kazhdan-Lusztig basis and satisfies a ``positivity condition''.