Characters and related distributions on reductive p-adic groups; distinguished representations

还原p进群的特征和相关分布；

• 批准号: 155502-2012
• 负责人: Murnaghan, Fiona
• 金额: $ 1.09万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=569474
• 关键词: Characters; related; distributions; reductive; adic

Our proposed research involves projects in the representation theory of reductive p-adic groups. Suppose that G is a group, r is a representation of G, where, for each g in G, r(g) is an invertible operator on a vector space V. If H is a subgroup of G, we say that the representation r is H-distinguished if the space of H-invariant linear functionals on V is nonzero. Reductive p-adic groups are matrix groups that are important in number theory. We are interested in studying H-distinguished representations of complex representations of reductive p-adic groups G, in the special case where H is the fixed points of an involution of G. Here, an involution of G is an automorphism of order 2. One aspect of our proposed research involves finding various ways to construct H-distinguished representations. Another aspect of our research involves the study of the behaviour of spherical characters of H-distinguished representations. These are functions on G whose definition is quite technical. Roughly speaking, these functions are determined by the various H-invariant linear functionals on the spaces of H-distinguished representations of G.

我们提出的研究项目涉及还原性表征理论