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Fake degrees: why coinvariant algebra and classical groups over finite fields?

Apologies if this is not research level math (in that it concerns well-known stuff), but I am having trouble tracking down sources that explain the following. References would be very appreciated. ...
Sam Hopkins's user avatar
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A combinatoric identity for characters of reductive groups

Let $G$ be a reductive group over an algebraic closed field (of char 0 if necessary). Let $T\subset G$ be a maximal torus and $S=\mathrm{Sym}^*(X(T))$ be the symmetric algebra of characters of $T$. ...
Fyy's user avatar
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