Identifier
Values
['A',1] => ([],1) => [2] => 1
['A',2] => ([(0,2),(1,2)],3) => [3,2] => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => [4,2] => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 2
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Description
The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition.
The Kronecker coefficient is the multiplicity $g_{\mu,\nu}^\lambda$ of the Specht module $S^\lambda$ in $S^\mu\otimes S^\nu$:
$$ S^\mu\otimes S^\nu = \bigoplus_\lambda g_{\mu,\nu}^\lambda S^\lambda $$
This statistic records the Kronecker coefficient $g_{\lambda,\lambda}^\lambda$.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.