Cohomology of special unitary groups and congruence subgroups

Abstract

We prove a homotopy invariance result for the first cohomology group of the special unitary group ${\mathrm{SU}}_3(F[t])$ with coefficients in irreducible representations of ${\mathrm{PGL}}_2(F)$. The main theorem establishes that this cohomology is naturally isomorphic to the corresponding cohomology of ${\mathrm{PGL}}_2(F)$.

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