the set Schubert varieties of flag variety is one-to-one Weyl groups via left cells,the Schubert varieties product the perverse sheaves on flag variety ,

my question is relations in Weyl groups can reflect to Schubert varieties and then perverse sheaves ,this relation is not $\le$,for example,$l(s*u)=l(u)+1$,where $s$ is a simple reflection,then we have $C(s)C(u)=C(su)$ ,where $C(?)$ is a left cell,what the relation between Schubert varieties labeled $s,u,su$ ,and intersection cohomology of them

there must be people study this question ,but I donot know, If you know,please tell me ,Thank you very much.