FUNCTION: SpJtMat - Jacobi-Trudi-type matrix

CALLING SEQUENCE:

SpJtMat(part)

CG[SpJtMat](part)

PARAMETERS:

part = any list denoting a partition

SYNOPSIS:

• The SpJtMat function computes the Jacobi-Trudi-type matrix which corresponds to the partition part. Its determinant gives the expansion of the symplectic Schur function Sp[part] in the h-basis.

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

EXAMPLES:

> with(CG):
> SpJtMat([7,4,3]);
 
                         [ h7  h8 + h6  h9 + h5 ]
                         [                      ]
                         [ h3  h4 + h2  h5 + h1 ]
                         [                      ]
                         [ h1   h2 + 1     h3   ]