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LSpice
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The coefficients do depend on $N$. A way to get around this and deal with "universal characters" was found by Koike and Terada (https://www.sciencedirect.com/science/article/pii/0021869387900998Young-diagrammatic methods for the representation theory of the classical groups of type $B_n$, $C_n$, $D_n$).

The coefficients do depend on $N$. A way to get around this and deal with "universal characters" was found by Koike and Terada (https://www.sciencedirect.com/science/article/pii/0021869387900998).

The coefficients do depend on $N$. A way to get around this and deal with "universal characters" was found by Koike and Terada (Young-diagrammatic methods for the representation theory of the classical groups of type $B_n$, $C_n$, $D_n$).

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Richard Stanley
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The coefficients do depend on $N$. A way to get around this and deal with "universal characters" was found by Koike and Terada (https://www.sciencedirect.com/science/article/pii/0021869387900998).