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MR813797 (87h:20084) 20G40 (20G05 20J06 55R40 55S10)
Kuhn, N. J.; Mitchell, S. A. The multiplicity of the Steinberg representation of ${\rm GL}\sb n{\bf F}\sb q$ in the symmetric algebra. Proc. Amer. Math. Soc. 96 (1986), no. 1, 1–6.
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