HighestRootWeylVectorPairing on CartanType
The symmetric bilinear form of the highest root with the Weyl vector, normalized so that the shortest roots have squared length 2.
Called as CombinatorialStat(x, "HighestRootWeylVectorPairing"). The head's page has its examples.
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FindStat St001678
The symmetric bilinear form applied to the highest root and the Weyl vector of a finite Cartan type.
| Object | Value |
|---|---|
['A',1] | 1 |
['A',2] | 2 |
['A',3] | 3 |
['A',4] | 4 |
['A',5] | 5 |
['A',6] | 6 |
['A',7] | 7 |
['A',8] | 8 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001678 has the rest.