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arXiv · 2112.08649

The Affine Closure of T^*(SL_n/U)

Boming Jia
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Abstract

We show that the affine closure of T^*(SL_n/U) has symplectic singularities, in the sense of Beauville. In the special case n=3, we show that the affine closure of T^*(SL_3/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^*(SL_3/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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Boming Jia. 2021-12-16. The Affine Closure of T^*(SL_n/U). https://arxiv.org/abs/2112.08649

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