The Affine Closure of T^*(SL_n/U)
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866917061783977984 |
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| author | Jia, Boming |
| author_facet | Jia, Boming |
| contents | 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). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_08649 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Affine Closure of T^*(SL_n/U) Jia, Boming Representation Theory 20G05 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). |
| title | The Affine Closure of T^*(SL_n/U) |
| topic | Representation Theory 20G05 |
| url | https://arxiv.org/abs/2112.08649 |