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edit approved Sep 29, 2014 at 6:44

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Restricting the Steinberg representation of SL_$SL_{2n}$ over a finite field to the symplectic group

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asked Sep 29, 2014 at 3:47

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Restricting the Steinberg representation of SL_{2n} over a finite field to the symplectic group

Let $\text{St}_n(\mathbb{F}_q)$ be the Steinberg module (over $\mathbb{C}$) for $\text{SL}_n(\mathbb{F}_q)$.

What is the irreducible decomposition of the restriction of $\text{St}_{2n}(\mathbb{F}_q)$ to the symplectic group $\text{Sp}_{2n}(\mathbb{F}_q)$?

rt.representation-theory finite-groups