SYMF::Sf2Char
--
converts a symmetric function into a virtual character
SYMF::Sf2Char(sf)
sf | - | any symmetric function |
The SYMF::Sf2Char
function converts a symmetric function into a virtual
character. This function is the inverse of Char2Sf
.
The SYMF::Sf2Char
function realizes the isomorphism between the linear
space of homogeneous symmetric functions of degree n
and class functions
on the symmetric group of degree n
(Frobenius isomorphism).
The result is a linear combination of cl[part]
where part
is a
partition.
>> muEC::SYMF::Sf2Char( s[3,1,1] );
cl[5] - 2 cl[2, 2, 1] + 6 cl[1, 1, 1, 1, 1]
>> muEC::SYMF::Sf2Char( p[3]*s[3] - e[4] );
cl[4] - cl[2, 2] - cl[3, 1] + 6 cl[3, 3] + cl[2, 1, 1] + 3 cl[3, 2, 1] - cl[1, 1, 1, 1] + 3 cl[3, 1, 1, 1]
Char2Sf
, SfInternal
, SfPlethysm
, SfZee
MuPAD Combinat, an open source algebraic combinatorics package