# splitCharacter -- Decomposes a symmetric polynomial as a sum of Schur functions

## Synopsis

• Usage:
splitCharacter(c)
• Inputs:
• c, , A Symmetric polynomial
• Outputs:
• p, ,

## Description

Expresses a symmetric polynomial c as a linear combination of Schur functions

 i1 : c=character({{1,1,1},{2}},4) 3 3 4 3 2 2 3 4 3 2 2 2 2 3 2 o1 = x x + x x x + 2x x x + 2x x x + x x x + 2x x x + 2x x x + 2x x x 0 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 ------------------------------------------------------------------------ 3 3 2 3 2 3 3 3 4 4 3 2 2 3 + x x + 2x x x + 2x x x + x x + x x x + x x x + 2x x x + 2x x x 0 2 0 1 2 0 1 2 1 2 0 1 2 0 1 3 0 1 3 0 1 3 ------------------------------------------------------------------------ 4 4 3 2 2 3 4 3 2 + x x x + x x x + 4x x x x + 5x x x x + 4x x x x + x x x + 2x x x 0 1 3 0 2 3 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3 ------------------------------------------------------------------------ 2 2 2 2 3 2 2 3 3 2 3 + 5x x x x + 5x x x x + 2x x x + 2x x x + 4x x x x + 2x x x + 0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 2 3 1 2 3 ------------------------------------------------------------------------ 4 4 3 2 2 2 2 3 2 3 2 2 2 x x x + x x x + 2x x x + 2x x x + 2x x x + 2x x x + 5x x x x + 0 2 3 1 2 3 0 1 3 0 1 3 0 1 3 0 2 3 0 1 2 3 ------------------------------------------------------------------------ 2 2 3 2 2 2 2 2 2 2 2 2 3 2 3 2 5x x x x + 2x x x + 2x x x + 5x x x x + 2x x x + 2x x x + 2x x x 0 1 2 3 1 2 3 0 2 3 0 1 2 3 1 2 3 0 2 3 1 2 3 ------------------------------------------------------------------------ 3 3 2 3 2 3 3 3 2 3 3 2 3 + x x + 2x x x + 2x x x + x x + 2x x x + 4x x x x + 2x x x + 0 3 0 1 3 0 1 3 1 3 0 2 3 0 1 2 3 1 2 3 ------------------------------------------------------------------------ 2 3 2 3 3 3 4 4 4 2x x x + 2x x x + x x + x x x + x x x + x x x 0 2 3 1 2 3 2 3 0 1 3 0 2 3 1 2 3 o1 : QQ[x ..x ] 0 3 i2 : splitCharacter(c) o2 = s + s 4,1,1 3,3 o2 : schurRing (QQ, s, 4)

## Ways to use splitCharacter :

• "splitCharacter(RingElement)"

## For the programmer

The object splitCharacter is .