Classification of supercuspidal unipotent representations by formal degrees

报告人:冯永琪, 荷兰内梅亨大学



Title:Classification of supercuspidal unipotent representations by formal degrees(joint-work with Eric Opdam and Maarten Solleveld)

Abstract:Let K be a non-archimedean local field, and let \mathbf{G} be a connected reductive group over K. For simplicity we assume that \mathbf{G} is quasi-split over K. Lusztig introduced the notion of unipotent representation for G=\mathbf{G}(K) which is based on the famous Deligne—Lusztig construction of representations for finite groups of Lie type. Assuming \mathbf{G} is adjoint and simple, Lusztig obtained a classification of unipotent representations for G which fits Langlands’ philosophy. For supercuspidal unipotent representations we have better result. Before Lusztig’s classification, Mark Reeder had shown that for adjoint simple exceptional groups which splits over K, one can partition their supercuspidal unipotent representations into L-packets such that the formal degree is a complete invariant for the L-packets.

In this talk, I will explain a result (joint with Eric Opdam and Maarten Solleveld) for classical groups analogous to Reeder’s for exceptional groups, and hence gives rise to a way to assign local Langlands parameters tor supercuspidal unipotent representations. Our Langlands parameters by formal degrees are essentially Lusztig’s parameters. This is also true in Reeder’s result.