Speaker: Daniel Wong (黄家裕) 香港中文大学深圳校区
Abstract: The Harish-Chandra Lefschetz principle says that there are similarities between the representation theories for real and $p$-adic groups. In this talk, we give one account of such resemblences by constructing an exact functor from the category of Harish-Chandra modules of $GL(n,\mathbb{C})$ to the category of finite-dimensional modules of graded Hecke algebra $\mathcal{H}_m$ of Type $A$. We will show that the functor preserves parabolically induced modules, standard modules, irreducible modules, unitary modules and Dirac series. It also links a Bernstein-Zelevinsky type functor in $\mathcal{H}_m$-module side to tensor decomposition problems on the $GL(n,\mathbb{C})$-module side. This is a joint work with Kei Yuen Chan.
Room: 216, East 32 Building.
Time: April 9, 10:30