The first cohomology group of SU_3(F[t]) with coefficients in irreducible representations of PGL_2(F) is naturally isomorphic to the corresponding cohomology of PGL_2(F).
Lagéométriedesgroupes classiques.3ièmeed., volume5of Ergeb.Math.Grenzgeb
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Cohomology of special unitary groups and congruence subgroups
The first cohomology group of SU_3(F[t]) with coefficients in irreducible representations of PGL_2(F) is naturally isomorphic to the corresponding cohomology of PGL_2(F).