TODO:
=====

* X_J^{-1} : left reps, LeftParabolicTransversal (emphasizing the lack of symmetry!)

* X_{JK}: double coset representatives

* X_{JKL}  with special case X_{JJJ}

* subgroups: X_J^M, X_{JK}^M, ...

* (complex) products:
   w * [w1, w2] = [w w1. w w2]
   X_J^M * X_M = X_J
   A * B = { a * b | a \in A, b \in B }
  
* intersections:
   X_J^{-1} \cap X_K = X_{JK},
   X_J \cap X_K = X_{J \cup K}

*  Y_J, Y_{JK}, Y_{JKL} ...

*  Z_J, Z_{JK}. Z_{JKL} ...

*  membership: w in X_J, w in Y_K ...

* LeftCells ...

* Bruhat intervals ...

* All of that wrt to ReflectionLength ...
-----------------------------------------------------------------------------

LongestCoxeterElement(ReflectionSubgroup(W, L)) -> 
LongestElement(W, L)

use: IsLeftDescent and IsRightDescent for clarification!