地点:数学高等研究院报告厅

时间: 6月3日，16:00 - 17:00

主讲人: Elad Zelingher (密歇根大学)

摘要：Whittaker models are important objects in the representation theory of reductive groups. In the last decade, degenerate Whittaker models of Speh representations of general linear groups have been used for new constructions of integral representations of L-functions. In this talk I will explain my results regarding explicit computations of special values of special degenerate Whittaker functions attached to Speh representations of two different types: unramified Speh representations and Speh representations of depth-zero supercuspidal representations. In both cases the formula expresses a special value of a distinguished Whittaker function in terms of modified Hall–Littlewood polynomials evaluated at the representation data. Moreover, In the depth-zero/finite field case, the special values are given by non-abelian versions of exotic Kloosterman sums. The proofs of these results rely on an integral construction, due to Ginzburg and Kaplan, for the tensor product L-function for GL_n×GL_m, generalizing the construction of Godement–Jacquet for the standard L-function.