Clifford algebra analogue of Cartan's theorem for symmetric pairs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918004497842176 |
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| author | Calvert, Kieran Grizelj, Karmen Krutov, Andrey Pandžić, Pavle |
| author_facet | Calvert, Kieran Grizelj, Karmen Krutov, Andrey Pandžić, Pavle |
| contents | We extend Kostant's results about $\mathfrak{g}$-invariants in the Clifford algebra $Cl(\mathfrak{g})$ of a complex semisimple Lie algebra $\mathfrak{g}$ to the relative case of $\mathfrak{k}$-invariants in the Clifford algebra $Cl(\mathfrak{p})$, where $(\mathfrak{g},\mathfrak{k})$ is a classical symmetric pair and $\mathfrak{p}$ is the $(-1)$-eigenspace of the corresponding involution. In this setup we prove the Cartan theorem for Clifford algebras, a relative transgression theorem, the Harish--Chandra isomorphism for $Cl(\mathfrak{p})$, and a relative version of Kostant's Clifford algebra conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Clifford algebra analogue of Cartan's theorem for symmetric pairs Calvert, Kieran Grizelj, Karmen Krutov, Andrey Pandžić, Pavle Representation Theory Differential Geometry 17B20, 22E60, 57T15, 57R91 We extend Kostant's results about $\mathfrak{g}$-invariants in the Clifford algebra $Cl(\mathfrak{g})$ of a complex semisimple Lie algebra $\mathfrak{g}$ to the relative case of $\mathfrak{k}$-invariants in the Clifford algebra $Cl(\mathfrak{p})$, where $(\mathfrak{g},\mathfrak{k})$ is a classical symmetric pair and $\mathfrak{p}$ is the $(-1)$-eigenspace of the corresponding involution. In this setup we prove the Cartan theorem for Clifford algebras, a relative transgression theorem, the Harish--Chandra isomorphism for $Cl(\mathfrak{p})$, and a relative version of Kostant's Clifford algebra conjecture. |
| title | Clifford algebra analogue of Cartan's theorem for symmetric pairs |
| topic | Representation Theory Differential Geometry 17B20, 22E60, 57T15, 57R91 |
| url | https://arxiv.org/abs/2504.20917 |