This talk will build on the previous talk of Hankyung Ko, but will be more elementary. It is based on joint work with Ko, Libedinsky, and Patimo. We introduce Demazure operators associated to double cosets. Through this lens we motivate the concept of "reduced expressions for double cosets," and we observe the switchback relations. Demazure operators are the technical and algebraic heart of (singular) Soergel bimodules, and we illustrate this with a theorem: that reduced expressions for the longest element contain the "deep bimodule" as a summand. Time permitting, we discuss recent work with Juteau and Young, where the "reduced expressions for the longest element in G(m,m,n)" were computed. We discuss implications of the deep bimodule theorem for the Spetses program.