An Artin parabolic subgroup of an Artin group 
is a conjugate 
of a standard subgroup 
generated by a subset 
of its standard generators, including 
. This usage is specific to Artin
groups and differs from the parabolic subgroups
of algebraic groups.
The intersection of an empty family of subgroups of 
is 
.
Conjecture for Artin Groups." Ann. Fac. Sci.
Toulouse Math. 23, 361-415, 2014.