FUNCTION:  StabChain - stabilizer chain for a Coxeter group,    
CALLING SEQUENCE:  StabChain(pg);,    
PARAMETERS:  pg = a permutation rePresentation of a Coxeter group
SYNOPSIS:   
  For a finite permutation group W, a stabilizer chain is a sequence of
  subgroups  W = W_0 > W_1 > W_2 > ... > W_m = {1} with the property that
  W_i is the subgroup of W_(i-1) that stabilizes some point b_i. Given a
  set of (right) coset representatives X_i for W_(i-1)/W_i, each element
  of W can be factored uniquely in the form w_m * ... * w_2 * w_1 with w_i
  in X_i. (By convention, permutations act on the right.)
  Let pg be a permutation rePresentation of a Coxeter group W acting on 
  cosets of a (proper) parabolic subgroup, in the format used by the
  function PermRep. That is, pg should be an unevaluated procedure call
  of the form,               permgroup(n, {s1=<perm1>, s2=<perm2>,...}),
  where each expression <perm_i> is a permutation of 1,...,n in disjoint
  cycle format. For a description of this format, see group[permgroup].,   
  each point-stabilizer in the chain is a parabolic subgroup. The output
  format is a list [[b_1,O_1,X_1],[b_2,O_2,X_2],...], where b_1,b_2,... are
  Base points as above, O_1 is the list of points in the W-Orbit of b_1,
  and X_1 is the corresponding list of minimum-length coset representatives
  for W modulo the stabilizer W_1 of b_1. More precisely, the j-th member
  of X_1 is a word of minimum length such that the corresponding product
  in W is a permutation sending b_1 to the j-th member of O_1. Similarly,
  O_2 is the list of points in the W_1-Orbit of b_2, and X_2 is the list
  of minimum-length coset representatives for W_1 modulo the stabilizer W_2
  of b_2 in W_1, and so on.,EXAMPLES:   
  pg:=PermRep(B3); sc:=StabChain(pg);,  sc[1];            yields
           [1, [1,2,3,4,5,6], [[],[3],[3,2],[3,2,1],[3,2,1,2],[3,2,1,2,3]]]
  sc[2]             yields     [2, [2,3,4,5], [[],[2],[2,1],[2,1,2]]]
  sc[3]             yields              [3, [3,4], [[],[1]]],    
SEE ALSO:  MultPerm, Perm2Word, PermRep, group[permgroup]):
