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arXiv · 1704.08344

Homological vanishing for the Steinberg representation

Avner Ash·Andrew Putman·Steven V Sam
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Abstract

For a field $k$, we prove that the $i$th homology of the groups $GL_n(k)$, $SL_n(k)$, $Sp_{2n}(k)$, $SO_{n,n}(k)$, and $SO_{n,n+1}(k)$ with coefficients in their Steinberg representations vanish for $n \geq 2i+2$.

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Avner Ash, Andrew Putman, Steven V Sam. 2017-04-26. Homological vanishing for the Steinberg representation. https://doi.org/10.1112/s0010437x18007029

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