Editing Canonical basis (section)

=== Hecke algebras ===
Let <math>(W,S)</math> be a [[Coxeter group]]. The corresponding [[Iwahori-Hecke algebra]] <math>H</math> has the standard basis <math>(T_w)_{w\in W}</math>, the group is partially ordered by the [[Bruhat order]] which is interval finite and has a dualization operation defined by <math>\overline{T_w}:=T_{w^{-1}}^{-1}</math>. This is a precanonical structure on <math>H</math> that satisfies the sufficient condition above and the corresponding canonical basis of <math>H</math> is the [[Kazhdan–Lusztig basis]]

: <math>C_w' = \sum_{y\leq w} P_{y,w}(v^2) T_w</math>

with <math>P_{y,w}</math> being the [[Kazhdan–Lusztig polynomial]]s.