We show that the affine closure T * (SL n /U) has symplectic singularities, in the sense of Beauville. In the special case n = 3, we show that the affine closure T * (SL 3 /U) is isomorphic to the closure of the minimal nilpotent orbit O min in so 8 . Moreover, the quasi-classical Gelfand-Graev action of the Weyl group W on T * (SL 3 /U) can be identified with the restriction to O min of E. Cartan's triality action on so 8 .
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