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
Speaker: 薛江维 武汉大学
Abstract: The notion ``selectivity" is first introduced by Chinburg and Friedman in 1999 to describe the phenomenon that certain quadratic orders tend to embed into some but not all maximal orders in a fixed indefinite quaternion algebra, as if they have selected some maximal order to embed into. This theory was further developed by Chan and Xu, Guo and Qin, and many others. However, most of the development focus on the indefinite case (i.e., when the quaternion algebra satisfies the Eichler condition). In this talk, we explain the generalization of the selectivity theory to the totally definite case and then apply it to obtain several refined class/type number formulas for totally definite quaternion orders. Such formulas enable us to prove certain divisibility results about these class/type numbers. This talk is based on joint works with Yucui Lin and Chia-Fu Yu.
Room: 216, East 32 Building.
Time: April 23, 10:30
Speaker: Nadir Matringe 上海纽约大学
Abstract: I will present an ongoing work with Omer Offen and Chang Yang on local global principles for certain periods of automorphic representations of inner forms of GL(n). In particular it implies the direct implication of a conjecture of Guo and Jacquet, without any local restriction on the global representation.
Room: 216, East 32 Building.
Time: April 29, 10:30