HELP FOR: A package for the Hecke algebra.

CALLING SEQUENCE:

HEKA[<function>](args)

<function>(args)

SYNOPSIS:

• This package provides functions to work with the Hecke algebra of the symmetric group. This algebra is generated by simple operators Ti's satisfying braid relations and the Hecke relation: Ti*Ti = (q1 + q2)*Ti - q1*q2

• The usual Hecke algebra is obtained by setting q1=q and q2=-1.

• A general element is expressed as a linear combination of A[perm], where perm is a permutation, with arbitrary coefficients.

• Whenever there is a conflict between a function name in HEKA and another name used in the same session, use the long form HEKA[<function>].

• The available functions are:

  Heka2Table	HekaAdd	HekaCharTable	HekaJucis
  HekaMinus	HekaMult	HekaNormal	HekaOnPol
  HekaOnX	HekaOnXfix	HekaYang	Rd2Heka
  Table2Heka

• For help with a particular function do either ?HEKA[<function>] or ?HEKA,<function> where <function> is one from the above list.

• Instead of HekaAdd, HekaMinus, HekaMult, one can use in short &?+ &?- &?*

EXAMPLES:

> with(HEKA):
> a:=q + u/t*A[3,1,2]:
> b:=t*A[2,1,3] - A[1,3,2]:
> HekaMult(a, b);
 
  q t A[2, 1, 3] + (- q1 q2 u - q) A[1, 3, 2] + (q1 u + q2 u) A[3, 1, 2]
 
           u A[3, 2, 1]
         - ------------
                 t