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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.19749 |
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| _version_ | 1866910765001211904 |
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| author | Elias, Ben |
| author_facet | Elias, Ben |
| contents | In this short, elementary note we prove that if a faithful reflection representation of a Coxeter group preserves an orthant, then that Coxeter group is a product of symmetric groups acting on its natural permutation representation. We also prove an affine analogue of this statement, where an orthant is preserved modulo an invariant sublattice. As a consequence, the existence of two different versions of the quantum geometric Satake equivalence is a purely type A phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coxeter groups preserving orthants Elias, Ben Representation Theory In this short, elementary note we prove that if a faithful reflection representation of a Coxeter group preserves an orthant, then that Coxeter group is a product of symmetric groups acting on its natural permutation representation. We also prove an affine analogue of this statement, where an orthant is preserved modulo an invariant sublattice. As a consequence, the existence of two different versions of the quantum geometric Satake equivalence is a purely type A phenomenon. |
| title | Coxeter groups preserving orthants |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2412.19749 |