FUNCTION: Perm2Demazure - Demazure element of the idCoxeter algebra
CALLING SEQUENCE:
- Perm2Demazure(perm)
- IDCA[Perm2Demazure](perm)
-
PARAMETERS:
- perm = any list denoting a permutation
SYNOPSIS:
- The Perm2Demazure function computes a special element of the idCoxeter
algebra.
- Given a permutation perm, with reduced decomposition s(i) s(j) s(k) ...
where s(i)=SgTranspo(i,n), then Perm2Demazure(perm) equals the product
(1 + Pi) &$* (1 + Pj) &$* (1 + Pk) &$* ...
- Perm2Demazure(perm) is the sum of all permutations below than perm (for
the Bruhat order).
- Whenever there is a conflict between the function name Perm2Demazure and
another name used in the same session, use the long form
IDCA['Perm2Demazure'].
EXAMPLES:
> with(IDCA):
> Perm2Demazure([2,3,1]);
A[2, 3, 1] + A[2, 1, 3] + A[1, 3, 2] + A[1, 2, 3]
SEE ALSO:
