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SchurRings :: classFunction

classFunction -- Converts symmetric function to class function

Synopsis

Usage:

ch = classFunction(f)
Inputs:
- f, a ring element, element of a Symmetric ring
Outputs:
- ch, a Class function

Description

Given a symmetric function f, homogeneous of degree N, the method computes the corresponding virtual character of the symmetric group S_N.

The character of the standard representation of S_5 is

i1 : R = symmetricRing(QQ,5);

i2 : classFunction(jacobiTrudi({4,1},R))

o2 = ClassFunction{{1, 1, 1, 1, 1} => 4}
                   {2, 1, 1, 1} => 2
                   {3, 1, 1} => 1
                   {3, 2} => -1
                   {5} => -1

o2 : ClassFunction

The character of the second exterior power of the standard representation of S_5 is

i3 : R = symmetricRing(QQ,5);

i4 : classFunction(jacobiTrudi({3,1,1},R))

o4 = ClassFunction{{1, 1, 1, 1, 1} => 6}
                   {2, 2, 1} => -2
                   {5} => 1

o4 : ClassFunction

See also

symmetricFunction -- Converts class function to symmetric function

Ways to use `classFunction` :

"classFunction(RingElement)"
classFunction(BasicList) -- Character of irreducible representation of symmetric group

For the programmer

The object classFunction is a method function.