The Affine Closure of T*(SLn/U)
Abstract
We show that the affine closure of T*(SLn/U) has symplectic singularities, in the sense of Beauville. In the special case n=3, we show that the affine closure of T*(SL3/U) is isomorphic to the closure of the minimal nilpotent adjoint orbit in so(8,C). Moreover, the quasi-classical Gelfand-Graev action of the Weyl group W on the affine closure of T*(SL3/U) can be identified with the restriction to the closure of the minimal nilpotent adjoint orbit of the triality action on so(8,C).
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