Purity Reigns Supreme

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Construction of automorphic Galois representations, II (2013, background): “In [C3] the relevant reference is the equality between the expressions (3.”
Dimensions of spaces of level one automorphic forms for split classical groups using the trace formula (2014, background): “r 1 and given Hodge weights. Remark 4.1.5. Except in the even orthogonal case with λ = k1e1 + ··· + k2ne2n and k2n = 0, it is known that any ψ ∈ Ψ(G) unr,λ sim is tempered also at the ﬁnite places by [Clo13]. 42 Remark 4.1.6. If Gis symplectic or even orthogonal, it has non-trivial center Zisomorphi”