internalProduct(ClassFunction,ClassFunction) -- Tensor product of virtual representations

Function: internalProduct
Usage:

ip = internalProduct(ch1,ch2)
Inputs:
- ch1, a Class function,
- ch2, a Class function,
Outputs:
- ip, a Class function,

Description

Given virtual characters ch1 and ch2, the method computes the character of the tensor product of corresponding virtual representations of the symmetric group.

i1 : ch1 = new ClassFunction from {{4,4} => 2, {8} => -1, {5,2,1} => 2, {3,2,2,1} => 1};

i2 : ch2 = new ClassFunction from {{2,2,2,2} => -4, {5,2,1} => 1, {3,2,2,1} => 3};

i3 : internalProduct(ch1,ch2)

o3 = ClassFunction{{3, 2, 2, 1} => 3}
                   {5, 2, 1} => 2

o3 : ClassFunction

i4 : ch1 * ch2

o4 = ClassFunction{{3, 2, 2, 1} => 3}
                   {5, 2, 1} => 2

o4 : ClassFunction

Ways to use this method:

internalProduct(ClassFunction,ClassFunction) -- Tensor product of virtual representations

The source of this document is in SchurRings.m2:3023:0.