  Let R be the polynomial ring in n variables, acted on by the symmetric group
S_n. Soergel constructed a full monoidal subcategory of R-bimodules which
categorifies the Hecke algebra, whose objects are now known as Soergel
bimodules. Soergel bimodules can be described as summands of Bott-Samelson
bimodules (attached to sequences of simple reflections), or as summands of
generalized Bott-Samelson bimodules (attached to sequences of parabolic
subgroups). A diagrammatic presentation of the category of Bott-Samelson
bimodules was given by the author and Khovanov in previous work. In this paper,
we extend it to a presentation of the category of generalized Bott-Samelson
bimodules. We also diagrammatically categorify the representations of the Hecke
algebra which are induced from trivial representations of parabolic subgroups.
  The main tool is an explicit description of the idempotent which picks out a
generalized Bott-Samelson bimodule as a summand inside a Bott-Samelson
bimodule. This description uses a detailed analysis of the reduced expression
graph of the longest element of S_n, and the semi-orientation on this graph
given by the higher Bruhat order of Manin and Schechtman.
