On $A$-parameters containing unitary lowest weight representations of $\mathrm{U}(p, q)$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915463938703360 |
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| author | Horinaga, Shuji |
| author_facet | Horinaga, Shuji |
| contents | In this paper, we determine all the Arthur packets containing an irreducible unitary lowest weight representation $π$ of real unitary group $G = \mathrm{U}(p, q)$, including non-scalar cases. Our methods are the Barbasch-Vogan parametrization of representations of $G$ and Trapa's algorithm to calculate the cohomologically induced representations. In particular, we show that an Arthur packet has at most one irreducible unitary lowest weight representation of $G$. As a consequence, if an irreducible unitary lowest weight representation $π$ exists in the Arthur packet of $ψ$, we give an explicit formula of the lowest $K$-type of $π$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07300 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $A$-parameters containing unitary lowest weight representations of $\mathrm{U}(p, q)$ Horinaga, Shuji Representation Theory Number Theory 17B10 11F55 In this paper, we determine all the Arthur packets containing an irreducible unitary lowest weight representation $π$ of real unitary group $G = \mathrm{U}(p, q)$, including non-scalar cases. Our methods are the Barbasch-Vogan parametrization of representations of $G$ and Trapa's algorithm to calculate the cohomologically induced representations. In particular, we show that an Arthur packet has at most one irreducible unitary lowest weight representation of $G$. As a consequence, if an irreducible unitary lowest weight representation $π$ exists in the Arthur packet of $ψ$, we give an explicit formula of the lowest $K$-type of $π$. |
| title | On $A$-parameters containing unitary lowest weight representations of $\mathrm{U}(p, q)$ |
| topic | Representation Theory Number Theory 17B10 11F55 |
| url | https://arxiv.org/abs/2502.07300 |