On the Lefschetz Principle for $\mathrm{GL}(n,\mathbb{C})$ and $\mathrm{GL}(m,\mathbb{Q}_p)$
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| Format: | Preprint |
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2023
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| _version_ | 1866912072772616192 |
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| author | Chan, Kei Yuen Wong, Kayue Daniel |
| author_facet | Chan, Kei Yuen Wong, Kayue Daniel |
| contents | We construct an exact functor from the category of Harish-Chandra modules of $\mathrm{GL}_n(\mathbb C)$ to the category of finite-dimensional modules of graded Hecke algebras of type A. We show that the functor preserves parabolically induced modules, standard modules, irreducible modules, unitary modules and Dirac series. We also use the functor to connect a Bernstein-Zelevinsky type functor for graded Hecke algebra side to the tensor product for $\mathrm{GL}_n(\mathbb C)$ side. Some applications are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15766 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Lefschetz Principle for $\mathrm{GL}(n,\mathbb{C})$ and $\mathrm{GL}(m,\mathbb{Q}_p)$ Chan, Kei Yuen Wong, Kayue Daniel Representation Theory 22E50, 22E47, 20C08 We construct an exact functor from the category of Harish-Chandra modules of $\mathrm{GL}_n(\mathbb C)$ to the category of finite-dimensional modules of graded Hecke algebras of type A. We show that the functor preserves parabolically induced modules, standard modules, irreducible modules, unitary modules and Dirac series. We also use the functor to connect a Bernstein-Zelevinsky type functor for graded Hecke algebra side to the tensor product for $\mathrm{GL}_n(\mathbb C)$ side. Some applications are also discussed. |
| title | On the Lefschetz Principle for $\mathrm{GL}(n,\mathbb{C})$ and $\mathrm{GL}(m,\mathbb{Q}_p)$ |
| topic | Representation Theory 22E50, 22E47, 20C08 |
| url | https://arxiv.org/abs/2305.15766 |