FUNCTION: Idca2Demazure - Demazure element of the idCoxeter algebra

CALLING SEQUENCE:

Idca2Demazure(e)

IDCA[Idca2Demazure](e)

PARAMETERS:

e = any element of the idCoxeter algebra

SYNOPSIS:

• The Idca2Demazure function converts an element of the idCoxeter algebra into a Demazure operator by replacing each A[perm] by the corresponding Demazure element of the idCoxeter algebra.

• Given a permutation perm, with reduced decomposition si sj sk ... where where si = SgTranspo(i), then Idca2Demazure(A[perm]) is equal to the product (1 + si) &$* (1 + sj) &$* (1 + sk) &$* ...

• Idca2Demazure(A[perm]) is the sum of all permutations below than perm (for the Bruhat order).

• Whenever there is a conflict between the function name Idca2Demazure and another name used in the same session, use the long form IDCA['Idca2Demazure'].

EXAMPLES:

> with(IDCA):
> Idca2Demazure(q*A[2,3,1] + A[1,2,3]);
 
      q A[2, 1, 3] + q A[2, 3, 1] + (q + 1) A[1, 2, 3] + q A[1, 3, 2]