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arxiv: 1704.08344 · v3 · pith:EJEAQRJOnew · submitted 2017-04-26 · 🧮 math.AT · math.GR· math.RT

Homological vanishing for the Steinberg representation

Avner Ash , Andrew Putman , Steven V Sam This is my paper
classification 🧮 math.AT math.GRmath.RT
keywords steinbergcoefficientsfieldgroupshomologicalhomologyproverepresentation
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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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