plethysm(RingElement,ClassFunction) -- Plethystic operations on class functions

Function: plethysm
Usage:

pl = plethysm(f,cF)

pl = plethysm(lambda,cF)
Inputs:
- a ring element
- a Class function

Description

These methods describe the result of applying plethystic operations to a virtual character of a symmetric group. These operations are described either via a symmetric function f, or a partition lambda. Since cF corresponds to an S_n- representation, the option GroupActing is irrelevant in this case.

i1 : cF = new ClassFunction from {{2} => 1, {1,1} => -1};

i2 : pl1 = plethysm({1,1},cF)

o2 = ClassFunction{{1, 1} => 1}
                   {2} => 1

o2 : ClassFunction

i3 : R = symmetricRing 5;

i4 : pl2 = plethysm(e_1+e_2,cF)

o4 = ClassFunction{{1, 1} => 0}
                   {2} => 2

o4 : ClassFunction

i5 : S = schurRing R;

i6 : symmetricFunction(cF,S)

o6 = -s
       1,1

o6 : S

i7 : symmetricFunction(pl1,S)

o7 = s
      2

o7 : S

i8 : symmetricFunction(pl2,S)

o8 = s  - s
      2    1,1

o8 : S

Ways to use this method:

plethysm(BasicList,ClassFunction)
plethysm(RingElement,ClassFunction) -- Plethystic operations on class functions

The source of this document is in SchurRings.m2:2279:0.