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arXiv · 2305.15766

On the Lefschetz Principle for $\mathrm{GL}(n,\mathbb{C})$ and $\mathrm{GL}(m,\mathbb{Q}_p)$

Kei Yuen Chan·Kayue Daniel Wong
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Abstract

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.

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BibTeXRIS

Kei Yuen Chan, Kayue Daniel Wong. 2023-05-25. On the Lefschetz Principle for $\mathrm{GL}(n,\mathbb{C})$ and $\mathrm{GL}(m,\mathbb{Q}_p)$. https://arxiv.org/abs/2305.15766

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