On the Lefschetz Principle for $\mathrm{GL}(n,\mathbb{C})$ and $\mathrm{GL}(m,\mathbb{Q}_p)$
Representation Theory
2024-10-16 v3
Abstract
We construct an exact functor from the category of Harish-Chandra modules of 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 side. Some applications are also discussed.
Cite
@article{arxiv.2305.15766,
title = {On the Lefschetz Principle for $\mathrm{GL}(n,\mathbb{C})$ and $\mathrm{GL}(m,\mathbb{Q}_p)$},
author = {Kei Yuen Chan and Kayue Daniel Wong},
journal= {arXiv preprint arXiv:2305.15766},
year = {2024}
}
Comments
v2: 38 pages, v3: Section 9.5 added, accepted version to appear in Israel Journal of Mathematics