Jesua Chavez, Institut de Mathématiques de Jussieu-Paris Rive Gauche: Howe correspondence between Harish-Chandra series
Referent: Jesua Chavez, Institut de Mathématiques de Jussieu-Paris Rive Gauche
Zeit: Dienstag, 18.12.2018, 17:15 h
Ort:Raum 48-208
Abstract:
Let Fq be a finite field with q elements and odd characteristic. A pair (G,G') of mutually centralized reductive subgroups of Sp2n(Fq) is called a reductive dual pair. By means of the Weil representation of Sp2n(Fq), Roger Howe introduced a correspondence Θ: R(G) → R(G') between the category of complex representations of these subgroups. Here we discuss how this correspondence relates the Harish-Chandra series of G to those of G'. If time allows, we will discuss how this correspondence can be expressed as a correspondence between unipotent Harish-Chandra series.