Nonzero $\mathfrak{n}$-cohomology of Totally Degenerate Limit of Discrete Series representations
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917496529879040 |
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| author | Lee, Jin Kunwoo |
| author_facet | Lee, Jin Kunwoo |
| contents | We show that a totally degenerate limit of discrete series representation admits a choice of n-cohomology group that is nonvanishing at a canonically defined degree. We then show that these groups satisfy Serre duality. This produces two n-cohomology groups, each for a totally degenerate limit of discrete series of U(n+1) and U(n), which are nonvanishing at the same degree. This suggests Gan-Gross-Prasad type branching laws for the TDLDS of unitary groups of any rank. We conclude by constructing an intertwining map of TDLDS for SU(2,1) and SU(1,1). This map will vanish on the minimal K type but induce a non-vanishing map of cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23102 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonzero $\mathfrak{n}$-cohomology of Totally Degenerate Limit of Discrete Series representations Lee, Jin Kunwoo Number Theory 11F70 (primary) 11F22, 11F75 (secondary) We show that a totally degenerate limit of discrete series representation admits a choice of n-cohomology group that is nonvanishing at a canonically defined degree. We then show that these groups satisfy Serre duality. This produces two n-cohomology groups, each for a totally degenerate limit of discrete series of U(n+1) and U(n), which are nonvanishing at the same degree. This suggests Gan-Gross-Prasad type branching laws for the TDLDS of unitary groups of any rank. We conclude by constructing an intertwining map of TDLDS for SU(2,1) and SU(1,1). This map will vanish on the minimal K type but induce a non-vanishing map of cohomology. |
| title | Nonzero $\mathfrak{n}$-cohomology of Totally Degenerate Limit of Discrete Series representations |
| topic | Number Theory 11F70 (primary) 11F22, 11F75 (secondary) |
| url | https://arxiv.org/abs/2507.23102 |