On exterior powers of reflection representations
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929597248962560 |
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| author | Hu, Hongsheng |
| author_facet | Hu, Hongsheng |
| contents | In 1968, R. Steinberg proved a theorem stating that the exterior powers of an irreducible reflection representation of a Euclidean reflection group are again irreducible and pairwise non-isomorphic. We extend this result to a more general context where the inner product invariant under the group action may not necessarily exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16946 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On exterior powers of reflection representations Hu, Hongsheng Representation Theory Combinatorics Group Theory Rings and Algebras 15A75, 05E10, 20C15, 20F55, 51F15 In 1968, R. Steinberg proved a theorem stating that the exterior powers of an irreducible reflection representation of a Euclidean reflection group are again irreducible and pairwise non-isomorphic. We extend this result to a more general context where the inner product invariant under the group action may not necessarily exist. |
| title | On exterior powers of reflection representations |
| topic | Representation Theory Combinatorics Group Theory Rings and Algebras 15A75, 05E10, 20C15, 20F55, 51F15 |
| url | https://arxiv.org/abs/2306.16946 |