Nilpotent orbits of height 2 and involutions in the affine Weyl group
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866914896195616768 |
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| author | Gandini, Jacopo Frajria, Pierluigi Moseneder Papi, Paolo |
| author_facet | Gandini, Jacopo Frajria, Pierluigi Moseneder Papi, Paolo |
| contents | Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B be a Borel subgroup of G. Then B acts with finitely many orbits on the variety N_2 of the nilpotent elements in g whose height is at most 2. We provide a parametrization of the B-orbits in N_2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description of the inclusion order among the B-orbit closures in terms of the Bruhat order on certain involutions in the affine Weyl group of g. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_01337 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Nilpotent orbits of height 2 and involutions in the affine Weyl group Gandini, Jacopo Frajria, Pierluigi Moseneder Papi, Paolo Algebraic Geometry Representation Theory 14M17, 14M27, 17B08 Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B be a Borel subgroup of G. Then B acts with finitely many orbits on the variety N_2 of the nilpotent elements in g whose height is at most 2. We provide a parametrization of the B-orbits in N_2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description of the inclusion order among the B-orbit closures in terms of the Bruhat order on certain involutions in the affine Weyl group of g. |
| title | Nilpotent orbits of height 2 and involutions in the affine Weyl group |
| topic | Algebraic Geometry Representation Theory 14M17, 14M27, 17B08 |
| url | https://arxiv.org/abs/1908.01337 |