Homology of loops on a splitting-rank symmetric space via the Geometric Satake for real groups
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917770023665664 |
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| author | O'Brien, John |
| author_facet | O'Brien, John |
| contents | Using Nadler's Geometric Satake Equivalence for real reductive groups, we obtain a description of the equivariant homology of the loop space of splitting-rank symmetric spaces in terms of the relative dual group of the space. The description is in line with Yun and Zhu's calculation for the loop space of a compact Lie group. The formula hints at a relative duality for these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09935 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homology of loops on a splitting-rank symmetric space via the Geometric Satake for real groups O'Brien, John Representation Theory Algebraic Geometry Number Theory Using Nadler's Geometric Satake Equivalence for real reductive groups, we obtain a description of the equivariant homology of the loop space of splitting-rank symmetric spaces in terms of the relative dual group of the space. The description is in line with Yun and Zhu's calculation for the loop space of a compact Lie group. The formula hints at a relative duality for these spaces. |
| title | Homology of loops on a splitting-rank symmetric space via the Geometric Satake for real groups |
| topic | Representation Theory Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2309.09935 |