FUNCTION: Sp2s - from the symplectic Schur basis to the Schur basis

CALLING SEQUENCE:

Sp2s(sf)

CG[Sp2s](sf)

PARAMETERS:

sf = any element in the symplectic Schur basis

SYNOPSIS:

• The Sp2s function converts any element expressed in the symplectic Schur basis into an element expressed in the basis of Schur functions.

• The result is a linear combination of Schur functions.

• Whenever there is a conflict between the function name Sp2s and another name used in the same session, use the long form CG['Sp2s'].

EXAMPLES:

> with(CG):
> Sp2s(Sp[6,3,2,1] - Sp[1,1,1]);
 
 s[6, 3, 2, 1] - s[6, 3, 1] - s[6, 2, 2]  -  s[6, 2, 1, 1]  -  s[5, 3, 2]
 
  - s[5, 3, 1, 1] - s[5, 2, 2, 1] -  2 s[5, 1] - 2 s[4, 2] - 2 s[4, 1, 1]
 
  + s[6, 2]  +  s[5, 3]  +  3 s[5, 2, 1]  +  s[6, 1, 1]  +  s[5, 1, 1, 1]
 
  + s[4, 3, 1] + s[4, 2, 2] + s[4, 2, 1, 1] + s[4] + s[3, 1] - s[3, 2, 1]
 
  - s[1, 1, 1] + s[1]