Irreducible unitary representations with non-zero relative Lie algebra cohomology of a Lie group of type f4(4)
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908287053594624 |
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| author | Paul, Pampa |
| author_facet | Paul, Pampa |
| contents | In this article, we have determined the irreducible unitary representations with non-zero relative Lie algebra cohomology and Poincare polynomials of cohomologies of these representations for a connected Lie group G with Lie algebra f4(4). We have also determined a necessary and sufficient condition for these representations to be discrete series representations and identified the discrete series representations and Borel-de Siebenthal discrete series representations among the irreducible unitary representations of G with non-zero relative Lie algebra cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21550 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducible unitary representations with non-zero relative Lie algebra cohomology of a Lie group of type f4(4) Paul, Pampa Representation Theory 22E46, 17B10, 17B20, 17B22, 17B25, 17B56 In this article, we have determined the irreducible unitary representations with non-zero relative Lie algebra cohomology and Poincare polynomials of cohomologies of these representations for a connected Lie group G with Lie algebra f4(4). We have also determined a necessary and sufficient condition for these representations to be discrete series representations and identified the discrete series representations and Borel-de Siebenthal discrete series representations among the irreducible unitary representations of G with non-zero relative Lie algebra cohomology. |
| title | Irreducible unitary representations with non-zero relative Lie algebra cohomology of a Lie group of type f4(4) |
| topic | Representation Theory 22E46, 17B10, 17B20, 17B22, 17B25, 17B56 |
| url | https://arxiv.org/abs/2503.21550 |