A Kronecker coefficient 
is the multiplicity of the complex Specht module 
in 
for the symmetric
group 
, where all three partitions
have the same size 
. Equivalently, writing 
for its group character,
 |
It is a nonnegative integer and is symmetric in the three partitions. For example, 
for 
contains the trivial
representation, the sign representation,
and the two-dimensional irreducible representation,
each once. Saxl's conjecture requires positivity
of these coefficients when the first two partitions
are the same staircase.
