Consider a function f in the variables 
The isobaric
divided difference of the function f with respect
to the variables 
and 
is
This operator sends polynomials to polynomials and preserves the degree.
Consider the polynomial ring 
in an infinite
sequence of indeterminates. For each 
, one can define
This operator still satisfy the braid relations but now
By product of simple operators, one has operators 
indexed by permutations,
which constitute a linear basis of the idCoxeter algebra
(IDCA ), i.e. the algebra generated
by the 
's.
The action on polynomials is given by the IdcaOnPol
function.
For this algebra, one has also a Yang-Baxter linear basis
(IdcaYang ).
