|Date: Tuesday, October 23, 2012
Location: 3096 East Hall (2:10 PM to 3:00 PM)
Title: What is ... Deligne-Lusztig theory
Abstract: epresentations of the group GL_n(K), where K is either a finite field or a local field, have been studied for many decades. (The local case is closely related to the structure of Galois groups of local fields via the local Langlands program, and therefore has important applications in number theory.) For finite K, irreducible representations of GL_n(K) were classified by J.A. Green in 1955, but a natural geometric construction of all such representations (which can be generalized to other reductive groups) was only discovered 20 years later by Deligne and Lusztig, who were motivated by the example of the "Drinfeld curve." Remarkably, even though the Drinfeld curve is used to construct representations of GL_2 of a finite field, it was discovered because of its connection with the Lubin-Tate tower, which yields a geometric realization of representations of GL_n of a local field. In my talk I will introduce all the aforementioned terms, give a brief history of the discoveries made by Drinfeld and Deligne-Lusztig, and outline some of the more recent applications of these ideas to p-adic representation theory.
Speaker: Dmitriy Boyarchenko
Institution: Univ of Michigan